AtlasRep Info for G2(3)
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→ ATLAS page for G2(3)
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→ Overview of Groups
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Representations for G = G2(3): (all refer to std. generators 1)
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| 1 |
G ≤ GL(14,2) |
character 14a |
| 2 |
G ≤ GL(78,2) |
character 78a |
| 3 |
G ≤ GL(90a,2) |
character 90a |
| 4 |
G ≤ GL(90b,2) |
character 90b |
| 5 |
G ≤ GL(90c,2) |
character 90c |
| 6 |
G ≤ GL(378,2) |
character 378a |
| 7 |
G ≤ GL(7a,3) |
character 7a |
| 8 |
G ≤ GL(7b,3) |
character 7b |
| 9 |
G ≤ GL(27a,3) |
character 27b |
| 10 |
G ≤ GL(27b,3) |
character 27a |
| 11 |
G ≤ GL(49,3) |
character 49a |
| 12 |
G ≤ GL(189a,3) |
character 189a |
| 13 |
G ≤ GL(189b,3) |
character 189b |
| 14 |
G ≤ GL(729,3) |
character 729a |
| 15 |
G ≤ GL(64a,4) |
character 64a |
| 16 |
G ≤ GL(14,ℤ) |
character 14a |
| 17 |
G ≤ GL(78,ℤ) |
character 78a |
| 18 |
G ≤ GL(91a,ℤ) |
character 91a |
| 19 |
G ≤ GL(91b,ℤ) |
character 91b |
| 20 |
G ≤ GL(91c,ℤ) |
character 91c |
| 21 |
G ≤ GL(104,ℤ) |
character 104a |
| 22 |
G ≤ GL(128,ℤ) |
character 64ab |
| 23 |
G ≤ GL(168,ℤ) |
character 168a |
| 24 |
G ≤ GL(182a,ℤ) |
character 182a |
| 25 |
G ≤ GL(182b,ℤ) |
character 182b |
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Programs for G = G2(3): (all refer to std. generators 1)
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class repres.:
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presentation:
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repr. cyc. subg.:
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std. gen. checker:
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automorphisms:
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maxes (all 10):
| 1 |
U3(3).2 |
| 2 |
U3(3).2 |
| 3 |
(3(1+2)+ × 32):2S4 |
| 4 |
(3(1+2)+ × 32):2S4 |
| 5 |
L3(3).2 |
| 6 |
L3(3).2 |
| 7 |
L2(8).3 |
| 8 |
23.L3(2) |
| 9 |
L2(13) |
| 10 |
2(1+4)+:32.2 |