Finite Group DatabasebetaFinite Group Databasebeta| order | 29766 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C41⋊((C11⋊D11)⋊C3) |
| unambiguous semidirect product | (C11⋊D451)⋊C3 |
| Fitting, socle, derived, Hall | C112×C41 ⋊ C2×C3 |
| Hall | C41×C112⋊C3 ⋊ C2 |
| Hall | C11⋊D451 ⋊ C3 |
| Hall | C112⋊C3 ⋊ D41 |
| Sylow | C112 ⋊ C3×D41 |
| Sylow | C41 ⋊ (C11⋊D11)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C41 | C2×C3 |
| LCS | G ▷ C112×C41 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 74 |
| transitive degree | μt(G) = 1353 |
A minimal faithful permutation representation — 2 generators on 74 points:
(1,2,4)(3,15,16,7,6,10)(5,24,19,11,12,29)(8,25,26,18,17,23)(9,30,28,20,21,14)(13,31,32,27,22,33)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74);(1,3,8,19,30,33,32,21,29,18,7)(2,5,13,25,6,14,28,15,17,27,11)(4,9,12,10,22,26,23,31,16,24,20)(34,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36)Polycyclic presentation:
2,3,11^2,41|c^a=c^10,d^a=d^10,e^a=e^40,c^b=c^7d^2,d^b=c^10d^3886 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29766, 14);