Finite Group DatabasebetaFinite Group Databasebeta| order | 23738 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D11869 |
| unambiguous semidirect product | C11⋊D1079 |
| unambiguous semidirect product | C13⋊D913 |
| unambiguous semidirect product | C83⋊D143 |
| Fitting, socle, derived, Hall | C11×C13×C83 ⋊ C2 |
| Hall | C13×C83 ⋊ D11 |
| Hall | C11×C83 ⋊ D13 |
| Hall | C11×C13 ⋊ D83 |
| Sylow | C83 ⋊ D143 |
| Sylow | C13 ⋊ D913 |
| Sylow | C11 ⋊ D1079 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C13×C83 | C2 |
| LCS | G ▷ C11×C13×C83 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 11869 |
A minimal faithful permutation representation — 2 generators on 107 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)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(2,11)(3,10)(4,9)(5,8)(6,7)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)(26,107)(27,106)(28,105)(29,104)(30,103)(31,102)(32,101)(33,100)(34,99)(35,98)(36,97)(37,96)(38,95)(39,94)(40,93)(41,92)(42,91)(43,90)(44,89)(45,88)(46,87)(47,86)(48,85)(49,84)(50,83)(51,82)(52,81)(53,80)(54,79)(55,78)(56,77)(57,76)(58,75)(59,74)(60,73)(61,72)(62,71)(63,70)(64,69)(65,68)(66,67)Polycyclic presentation:
2,11,13,83|b^a=b^10,c^a=c^12,d^a=d^825936 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23738, 8);