Finite Group DatabasebetaFinite Group Databasebeta| order | 34914 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#26042790 |
| Fitting, socle, derived, Hall | C3×C232 ⋊ C2×C11 |
| Hall | C3×#19154124 ⋊ C2 |
| Hall | #19154124 ⋊ D3 |
| Hall | C3⋊(C23⋊D23) ⋊ C11 |
| Sylow | C232 ⋊ D3×C11 |
| Sylow | C3 ⋊ #26042790 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C232 | C2×C11 |
| LCS | G ▷ C3×C232 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 759 |
A minimal faithful permutation representation — 2 generators on 49 points:
(2,3)(5,8,9,16,17,24,19,20,10,21,22,6,7,11,12,23,18,13,25,14,15,26)(28,32,33,38,45,48,49,34,31,41,42,29,30,37,39,44,43,47,40,35,36,46);(1,2,3)(4,5,7,10,9,13,15,23,12,18,20,26,22,25,24,16,17,21,19,11,14,8,6)(27,28,31,36,43,44,49,46,33,40,32,38,39,30,34,37,42,47,45,48,41,35,29)Polycyclic presentation:
2,11,3,23^2|c^a=c^2,d^a=d^22,e^a=e^22,d^b=d^2,e^b=e^13105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34914, 61);