Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for F₃₊

Name:

F3+

Group order:

1255205709190661721292800 = 2²¹ ⋅ 3¹⁶ ⋅ 5² ⋅ 7³ ⋅ 11 ⋅ 13 ⋅ 17 ⋅ 23 ⋅ 29

Number of classes:

108

InfoText value:

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

Maximal subgroups:

	Order	Index	Structure	Name
1	4089470473293004800	306936	Fi23	Fi23
2	258247006617600	4860485028	2.Fi22.2	2.Fi22.2
3	89139236659200	14081405184	(3 × O8+(3):3):2	(3xO8+(3):3):2
4	25015379558400	50177360142	O10−(2)	O10-(2)
5	10028164124160	125168046080	37.O7(3)	3^7.O7(3)
6	4848782653440	258870277120	31+10:U5(2):2	3^(1+10):U5(2):2
7	501397585920	2503413946215	211.M24	F3+M7
8	220723937280	5686767482760	22.U6(2).3.2	2^2.U6(2).3.2
9	160526499840	7819305288795	21+12.31.U4(3).22'	2^(1+12).3_1.U4(3).2_2'
10	17907435936	70094105804800	33.[310].GL3(3)	3^3.[3^10].GL3(3)
11	13774950720	91122337546240	32.34.38.(A5 × 2A4).2	3^2.3^4.3^8.(A5x2A4).2
12	12541132800	100087107696576	(A4 × O8+(2).3).2	(A4xO8+(2).3).2
13	8060774400	155717756992512	He.2	He.2
14	8060774400	155717756992512	He.2	F3+M14
15	1981808640	633363728392395	23+12.(L3(2) × A6)	2^(3+12).(L3(2)xA6)
16	1981808640	633363728392395	26+8.(S3 × A8)	2^(6+8).(S3xA8)
17	152845056	8212275503308800	(32:2 × G2(3)).2	(3^2:2xG2(3)).2
18	21772800	57650174033227776	(A5 × A9):2	(A5xA9):2
19	544320	2306006961329111040	A6 × L2(8):3	A6xL2(8):3
20	105840	11859464372549713920	7:6 × A7	7:6xA7
21	12096	103770313259809996800	U3(3).2	U3(3).2
22	12096	103770313259809996800	U3(3).2	U3(3).2
23	2184	574727888823563059200	L2(13).2	L2(13).2
24	2184	574727888823563059200	L2(13).2	L2(13).2
25	406	3091639677809511628800	29:14	29:14

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
5	28800	43583531569120198656	F3+N5	F3+N5
7	12348	101652551764711833600	71+2:(S3 × 6)	7^(1+2):(S3x6)
11	1320	950913416053531607040	(A4 × 11:5).2	(A4x11:5).2
13	2808	447010580196104601600	(32:2 × 13:6).2	(3^2:2x13:6).2
17	272	4614726872024491622400	17:16	17:16
23	253	4961287388105382297600	23:11	23:11
29	406	3091639677809511628800	29:14	29:14

Available Brauer tables:

p
11	dec. matrix (PDF)
17	dec. matrix (PDF)
23	dec. matrix (PDF)
29	dec. matrix (PDF)

Group constructions in GAP:

AtlasGroup( "Fi24'" ), AtlasSubgroup( "Fi24'.2", 1 )

Stored class fusions from this table:

F₃₊.2

Stored class fusions to this table:

2.Fi₂₂.2, 2².U₆(2).3.2, 2¹⁺¹².3₁.U₄(3).2₂', 2³⁺¹².(L₃(2) × A₆), 2⁶⁺⁸.(S₃ × A₈), 3.F₃₊, 3².3⁴.3⁸.(A₅ × 2A₄).2, 3³.[3¹⁰].GL₃(3), 3⁷.O₇(3), 3¹⁺¹⁰:U₅(2):2, 3¹⁺¹⁰₊:2¹⁺⁶₋:3¹⁺²₊:2S₄, 7:6 × A₇, 7¹⁺²:(S₃ × 6), 17:16, 23:11, 29:14, (3²:2 × 13:6).2, (3²:2 × G₂(3)).2, (3 × O₈⁺(3):3):2, (A₄ × 11:5).2, (A₄ × O₈⁺(2).3).2, (A₅ × A₉):2, (D₁₀ × A₉).2, A₆ × L₂(8):3, 2¹¹.M₂₄, He.2, F₃₊N5, Fi₂₃, He.2, L₂(13).2, O₁₀⁻(2), U₃(3).2

File created automatically by GAP on 13-Mar-2024.