Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for M

Name:

M

Group order:

808017424794512875886459904961710757005754368000000000 = 2⁴⁶ ⋅ 3²⁰ ⋅ 5⁹ ⋅ 7⁶ ⋅ 11² ⋅ 13³ ⋅ 17 ⋅ 19 ⋅ 23 ⋅ 29 ⋅ 31 ⋅ 41 ⋅ 47 ⋅ 59 ⋅ 71

Number of classes:

194

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r.

Maximal subgroups:

	Order	Index	Structure	Name
1	8309562962452852382355161088000000	97239461142009186000	2.B	2.B
2	139511839126336328171520000	5791748068511982636944259375	21+24.Co1	2^1+24.Co1
3	7531234255143970327756800	107288845018015770869760000000	3.F3+.2	3.F3+.2
4	1836779512410596494540800	439909863614532427326210000000	22.2E6(2).3.2	2^2.2E6(2).3.2
5	1577011055923770163200	512372707698741056749515292734375	210+16.O10+(2)	2^(10+16).O10+(2)
6	50472333605150392320	16009115629875684006343550944921875	22+11+22.(M24 × S3)	2^(2+11+22).(M24xS3)
7	2859230155080499200	282599644298926271851701207040000000	31+12.2.Suz.2	3^(1+12).2.Suz.2
8	2061452360684666880	391965121389536908413379198941796875	25+10+20.(S3 × L5(2))	2^(5+10+20).(S3xL5(2))
9	544475663327232000	1484028541986258159045049319424000000	S3 × Th	S3xTh
10	199495389743677440	4050306254358548053604918389065234375	2[39].(L3(2) × 3.S6)	2^[39].(L3(2)x3.S6)
11	133214132225341440	6065553341050124859256025907200000000	38.O8−(3).23	3^8.O8-(3).2_3
12	5460618240000000	147971784380684498443615773616452403200	(D10 × HN).2	(D10xHN).2
13	2139341679820800	377694424605514962329798663208960000000	(32:2 × O8+(3)).S4	(3^2:2xO8+(3)).S4
14	49093924366080	16458603283969466072643078298009600000000	32+5+10.(M11 × 2S4)	3^(2+5+10).(M11x2S4)
15	11604018486528	69632552355255433384259177414656000000000	33+2+6+6:(L3(3) × SD16)	3^(3+2+6+6):(L3(3)xSD16)
16	378000000000	2137612234906118719276348954925160732819456	51+6:2.J2.4	5^(1+6):2.J2.4
17	169276262400	4773365227577903302562875496013496320000000	(7:3 × He):2	(7:3xHe):2
18	28740096000	28114639032330054704286996987125956608000000	(A5 × A12):2	(A5xA12):2
19	11625000000	69506875251140892549372895050469742538129408	53+3.(2 × L3(5))	5^(3+3).(2xL3(5))
20	2239488000	360804534248235702038349794668116443136000000	(A6 × A6 × A6).(2 × S4)	(A6xA6xA6).(2xS4)
21	1985679360	406922407046882370719943377445244108800000000	(A5 × U3(8):3):2	(A5xU3(8):3):2
22	1125000000	718237710928455889676853248854854006227337216	52+2+4:(S3 × GL2(5))	5^(2+2+4):(S3xGL2(5))
23	658022400	1227948204794415624584299721349471928320000000	(L3(2) × S4(4):2).2	(L3(2)xS4(4):2).2
24	508243680	1589822867634109834649512818264086937600000000	71+4:(3 × 2.S7)	7^(1+4):(3x2.S7)
25	302400000	2672015293632648399095436193656450916024320000	(52:[24] × U3(5)).S3	(5^2:[2^4]xU3(5)).S3
26	125452800	6440808214679248895891202946141582786560000000	(L2(11) × M12):2	(L2(11)xM12):2
27	72576000	11133397056802701662897650806901878816768000000	(A7 × (A5 × A5):22):2	(A7x(A5xA5):2^2):2
28	58500000	13812263671701074801477947093362577042833408000	54:(3 × 2.L2(25)).2	5^4:(3x2.L2(25)).2
29	33882912	23847343014511647519742692273961304064000000000	72+1+2:GL2(7)	7^(2+1+2):GL2(7)
30	11404800	70848890361471737854803232407557410652160000000	M11 × A6.22	M11xA6.2^2
31	10368000	77933779397618911640283555648313151717376000000	(S5 × S5 × S5):S3	(S5xS5xS5):S3
32	1742400	463738191456905920504166612122193960632320000000	(L2(11) × L2(11)):4	(L2(11)xL2(11)):4
33	1476384	547294894007597532814267768386619441152000000000	132:2.L2(13).4	13^2:2.L2(13).4
34	1185408	681636554498124591605978620830727274496000000000	(72:(3 × 2A4) × L2(7)).2	(7^2:(3x2A4)xL2(7)).2
35	876096	922293247309099546038858646725599428608000000000	(13:6 × L3(3)).2	(13:6xL3(3)).2
36	632736	1277021419351060909899958126235445362688000000000	131+2:(3 × 4S4)	13^(1+2):(3x4S4)
37	249600	3237249298054939406596393850006853994414080000000	U3(4).4	U3(4).4
38	178920	4516082186421377575935948496320762111590400000000	L2(71)	L2(71)
39	72600	11129716594965742092099998690932655055175680000000	112:(5 × 2.A5)	11^2:(5x2.A5)
40	34440	23461597700189107894496512919910300726067200000000	L2(41)	L2(41)
41	24360	33169845024405290471529552748838701026508800000000	L2(29).2	L2(29).2
42	16464	49077831923864970595630460699812363763712000000000	72:2L2(7)	7^2:2psl(2,7)
43	6840	118131202455338139749482442245864145761075200000000	L2(19).2	L2(19).2
44	2184	369971348349135932182445011429354742218752000000000	L2(13).2	L2(13).2
45	1711	472248641025431254170929225576686590885888000000000	59:29	59:29
46	1640	492693551703971265784426771318116315247411200000000	41:40	41:40

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
5	187500000	4309426265570735338061119493129124037364023296	MN5	MN5
7	4235364	190778744116093180157941538191690432512000000000	[76]:(6 × 6)	[7^6]:(6x6)
11	72600	11129716594965742092099998690932655055175680000000	112:(5 × 2.A5)	11^2:(5x2.A5)
13	632736	1277021419351060909899958126235445362688000000000	131+2:(3 × 4S4)	13^(1+2):(3x4S4)
41	1640	492693551703971265784426771318116315247411200000000	41:40	41:40
47	2162	373736089174150266367465265939736705368064000000000	2 × 47:23	2x47:23
59	1711	472248641025431254170929225576686590885888000000000	59:29	59:29

Available Brauer tables:

p
17	dec. matrix (PDF)
19	dec. matrix (PDF)
23	dec. matrix (PDF)
31	dec. matrix (PDF)

Stored class fusions to this table:

2.(2 × F₄(2)).2, 2.B, 2¹⁺²⁴.Co₁, 2².²E₆(2).3.2, 2^2+11+22.(M₂₄ × S₃), 2^5+10+20.(S₃ × L₅(2)), 2¹⁰⁺¹⁶.O₁₀⁺(2), 2^[39].(L₃(2) × 3.S₆), 2 × 47:23, 3.F₃₊.2, 3⁸.O₈⁻(3).2₃, 3¹⁺¹².2.Suz.2, 3²⁺⁵⁺¹⁰.(M₁₁ × 2S₄), 3^3+2+6+6:(L₃(3) × SD₁₆), 5⁴:(3 × 2.L₂(25)).2, 5¹⁺⁶:2.J₂.4, 5²⁺²⁺⁴:(S₃ × GL₂(5)), 5³⁺³.(2 × L₃(5)), 7¹⁺⁴.2A₇, 7²:2L₂(7), 7¹⁺⁴:(3 × 2.S₇), 7²⁺¹⁺²:GL₂(7), 11²:(5 × 2.A₅), 13²:2.L₂(13).4, 13¹⁺²:(3 × 4S₄), 41:40, 59:29, (3²:2 × O₈⁺(3)).S₄, (3¹⁺²:2² × G₂(3)):2, (5²:[2⁴] × U₃(5)).S₃, (7:3 × He):2, (7²:(3 × 2A₄) × L₂(7)).2, (11:5 × M₁₂):2, (13:6 × L₃(3)).2, (A₅ × A₁₂):2, (A₅ × U₃(8):3):2, (A₆ × A₆ × A₆).(2 × S₄), (A₇ × (A₅ × A₅):2²):2, (D₁₀ × HN).2, (L₂(11) × L₂(11)):4, (L₂(11) × M₁₂):2, (L₃(2) × S₄(4):2).2, (QD₁₆ × ²F₄(2)').2, (S₃ × 2.Fi₂₂).2, (S₅ × S₅ × S₅):S₃, L₂(13).2, L₂(19).2, L₂(29).2, L₂(41), L₂(71), M₁₁ × A₆.2², MN5, S₃ × Th, U₃(4).4, [7⁶]:(6 × 6)

File created automatically by GAP on 20-May-2025.