Finite Group DatabasebetaFinite Group Databasebeta| order | 26934 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Sylow | C672 ⋊ D3 |
| derived, Hall | #27212174 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #27212174 | C2 |
| Fitting, socle | C672 | D3 |
| LCS | G ▷ #27212174 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 134 |
| transitive degree | μt(G) = 134 |
A minimal faithful permutation representation — 2 generators on 134 points:
(1,7,18,28,56,72,108,119,122,134,105,128,81,116,57,95,37,67,22,29,60,73,111,120,133,123,125,104,106,75,78,30,43,94,89,115,64,74,112,83,86,55,58,31,34,8,13,45,76,91,92,63,65,39,41,21,23,9,11,2,3,14,32,47,80,97,103,129,77,118,53,96,33,69,19,44,10,15,36,48,84,99,126,130,132,131,124,121,109,101,85,50,61,93,40,49,88,100,127,107,110,79,82,51,54,16,25,68,102,113,114,87,90,59,62,35,38,17,20,4,6,27,52,70,66,117,42,98,24,71,12,46,5,26);(3,5,10)(4,7,9)(6,12,22)(8,15,21)(11,19,18)(13,24,40)(14,26,17)(16,29,39)(20,33,36)(23,37,32)(25,42,64)(27,44,35)(28,46,31)(30,49,63)(34,53,60)(38,57,56)(41,61,52)(43,66,90)(45,67,59)(47,69,55)(48,71,51)(50,74,91)(54,77,88)(58,81,84)(62,85,80)(65,89,76)(68,93,87)(70,95,83)(72,96,79)(73,98,75)(78,103,112)(82,105,111)(86,109,108)(92,114,102)(94,115,113)(97,116,107)(99,118,104)(100,117,101)(106,122,127)(110,124,126)(119,128,123)(120,129,121)(125,132,133)(130,134,131)Polycyclic presentation:
2,3,67^2|b^a=b^2,c^a=d,d^a=c,c^b=c^29,d^b=d^37850 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26934, 8);