Finite Group DatabasebetaFinite Group Databasebeta| order | 35926 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D17963 |
| unambiguous semidirect product | C11⋊D1633 |
| unambiguous semidirect product | C23⋊D781 |
| unambiguous semidirect product | C71⋊D253 |
| Fitting, socle, derived, Hall | C11×C23×C71 ⋊ C2 |
| Hall | C23×C71 ⋊ D11 |
| Hall | C11×C71 ⋊ D23 |
| Hall | C11×C23 ⋊ D71 |
| Sylow | C71 ⋊ D253 |
| Sylow | C23 ⋊ D781 |
| Sylow | C11 ⋊ D1633 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C23×C71 | C2 |
| LCS | G ▷ C11×C23×C71 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 17963 |
A minimal faithful permutation representation — 2 generators on 105 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);(2,11)(3,10)(4,9)(5,8)(6,7)(13,34)(14,33)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(36,105)(37,104)(38,103)(39,102)(40,101)(41,100)(42,99)(43,98)(44,97)(45,96)(46,95)(47,94)(48,93)(49,92)(50,91)(51,90)(52,89)(53,88)(54,87)(55,86)(56,85)(57,84)(58,83)(59,82)(60,81)(61,80)(62,79)(63,78)(64,77)(65,76)(66,75)(67,74)(68,73)(69,72)(70,71)Polycyclic presentation:
2,11,23,71|b^a=b^10,c^a=c^22,d^a=d^708983 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35926, 9);