Finite Group DatabasebetaFinite Group Databasebeta| order | 23606 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D11803 |
| unambiguous semidirect product | C11⋊D1073 |
| unambiguous semidirect product | C29⋊D407 |
| unambiguous semidirect product | C37⋊D319 |
| Fitting, socle, derived, Hall | C11×C29×C37 ⋊ C2 |
| Hall | C29×C37 ⋊ D11 |
| Hall | C11×C37 ⋊ D29 |
| Hall | C11×C29 ⋊ D37 |
| Sylow | C37 ⋊ D319 |
| Sylow | C29 ⋊ D407 |
| Sylow | C11 ⋊ D1073 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C29×C37 | C2 |
| LCS | G ▷ C11×C29×C37 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 11803 |
A minimal faithful permutation representation — 2 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77);(2,11)(3,10)(4,9)(5,8)(6,7)(13,40)(14,39)(15,38)(16,37)(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)(42,77)(43,76)(44,75)(45,74)(46,73)(47,72)(48,71)(49,70)(50,69)(51,68)(52,67)(53,66)(54,65)(55,64)(56,63)(57,62)(58,61)(59,60)Polycyclic presentation:
2,11,29,37|b^a=b^10,c^a=c^28,d^a=d^365903 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23606, 8);