Finite Group DatabasebetaFinite Group Databasebeta| order | 26934 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C67 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C672 ⋊ C2×C3 |
| Hall | #27212174 ⋊ C2 |
| Hall | C67⋊D67 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C672 | C2×C3 |
| LCS | G ▷ C672 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 134 |
| transitive degree | μt(G) = 201 |
A minimal faithful permutation representation — 2 generators on 134 points:
(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,59)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,54,55,49,40,64)(34,61,62,50,48,57)(37,42,60,52,53,58)(51,65,66,63,56,67)(69,73,74,70,71,75)(72,81,82,76,77,91)(78,94,95,84,85,108)(79,93,89,87,83,80)(86,113,114,97,98,126)(88,111,112,100,96,105)(90,92,110,102,103,106)(99,122,121,107,116,132)(101,129,130,117,115,123)(104,109,128,118,119,124)(120,127,133,125,131,134);(1,2,5,11,19,32,45,15,26,14,25,40,56,66,47,60,64,61,46,53,18,29,39,41,57,63,50,33,20,4,8,13,23,37,52,35,22,7,6,12,21,34,51,62,28,43,44,27,42,31,48,55,58,59,67,65,54,36,10,16,24,38,49,30,17,9,3)(68,69,72,78,86,99,103,77,83,91,105,121,133,131,98,115,122,124,126,130,95,110,111,94,109,125,118,102,89,74,73,79,88,101,117,100,87,71,75,80,90,104,120,119,85,96,106,108,123,114,128,116,129,113,127,134,132,112,82,93,81,92,107,97,84,76,70)Polycyclic presentation:
2,3,67^2|c^a=c^66,d^a=d^66,c^b=c^29,d^b=d^37754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26934, 14);