Finite Group DatabasebetaFinite Group Databasebeta| order | 34914 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C11⋊((C23⋊D23)⋊C3) |
| unambiguous semidirect product | (C11⋊(C23⋊D23))⋊C3 |
| Fitting, socle, derived, Hall | C11×C232 ⋊ C2×C3 |
| Hall | C11×C232⋊C3 ⋊ C2 |
| Hall | C11⋊(C23⋊D23) ⋊ C3 |
| Hall | C232⋊C3 ⋊ D11 |
| Sylow | C232 ⋊ C3×D11 |
| Sylow | C11 ⋊ (C23⋊D23)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C232 | C2×C3 |
| LCS | G ▷ C11×C232 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 80 |
| transitive degree | μt(G) = 759 |
A minimal faithful permutation representation — 2 generators on 80 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13,15)(14,29,30,18,19,43)(16,41,42,23,24,57)(17,22,46,27,28,40)(20,52,53,33,34,60)(21,56,25,36,37,31)(26,62,63,45,39,77)(32,47,55,44,51,35)(38,74,48,58,59,67)(49,50,76,70,61,64)(54,65,73,68,72,78)(66,80,69,75,79,71);(1,2,4,6,8,10,11,9,7,5,3)(12,14,20,35,40,64,78,37,57,74,79,63,77,80,59,42,56,73,76,46,55,33,18)(13,16,25,29,48,68,52,71,70,32,45,27,17,26,44,49,69,34,54,67,19,31,23)(15,21,38,60,50,62,28,47,66,72,30,41,24,43,65,75,51,22,39,61,53,58,36)Polycyclic presentation:
2,3,11,23^2|c^a=c^10,d^a=d^22,e^a=e^22,d^b=d^7e^3,e^b=d^4e^15989 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34914, 75);