Finite Group DatabasebetaFinite Group Databasebeta| order | 33418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D16709 |
| unambiguous semidirect product | C11⋊D1519 |
| unambiguous semidirect product | C31⋊D539 |
| unambiguous semidirect product | C49⋊D341 |
| Fitting, derived, Hall | C11×C31×C49 ⋊ C2 |
| Hall | C31×C49 ⋊ D11 |
| Hall | C11×C49 ⋊ D31 |
| Hall | C11×C31 ⋊ D49 |
| Sylow | C49 ⋊ D341 |
| Sylow | C31 ⋊ D539 |
| Sylow | C11 ⋊ D1519 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C11×C31×C49 | C2 |
| Frattini | C7 | D2387 |
| socle | C7×C11×C31 | D7 |
| LCS | G ▷ C11×C31×C49 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 16709 |
A minimal faithful permutation representation — 2 generators on 91 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);(2,49)(3,48)(4,47)(5,46)(6,45)(7,44)(8,43)(9,42)(10,41)(11,40)(12,39)(13,38)(14,37)(15,36)(16,35)(17,34)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)(51,60)(52,59)(53,58)(54,57)(55,56)(62,91)(63,90)(64,89)(65,88)(66,87)(67,86)(68,85)(69,84)(70,83)(71,82)(72,81)(73,80)(74,79)(75,78)(76,77)Polycyclic presentation:
2,7,11,31,7|b^7=e^6,b^a=b^6e,c^a=c^10,d^a=d^30,e^a=e^68356 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33418, 8);