Finite Group DatabasebetaFinite Group Databasebeta| order | 33374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D16687 |
| unambiguous semidirect product | C11⋊D1517 |
| unambiguous semidirect product | C37⋊D451 |
| unambiguous semidirect product | C41⋊D407 |
| Fitting, socle, derived, Hall | C11×C37×C41 ⋊ C2 |
| Hall | C37×C41 ⋊ D11 |
| Hall | C11×C41 ⋊ D37 |
| Hall | C11×C37 ⋊ D41 |
| Sylow | C41 ⋊ D407 |
| Sylow | C37 ⋊ D451 |
| Sylow | C11 ⋊ D1517 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C37×C41 | C2 |
| LCS | G ▷ C11×C37×C41 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 16687 |
A minimal faithful permutation representation — 2 generators on 89 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);(2,11)(3,10)(4,9)(5,8)(6,7)(13,48)(14,47)(15,46)(16,45)(17,44)(18,43)(19,42)(20,41)(21,40)(22,39)(23,38)(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)(50,89)(51,88)(52,87)(53,86)(54,85)(55,84)(56,83)(57,82)(58,81)(59,80)(60,79)(61,78)(62,77)(63,76)(64,75)(65,74)(66,73)(67,72)(68,71)(69,70)Polycyclic presentation:
2,11,37,41|b^a=b^10,c^a=c^36,d^a=d^408345 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33374, 8);