Finite Group DatabasebetaFinite Group Databasebeta| order | 34892 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic8723 |
| unambiguous semidirect product | C11⋊Dic793 |
| derived, Hall | C11×C13×C61 ⋊ C4 |
| Hall | C13×C61 ⋊ Dic11 |
| Hall | C11×C61 ⋊ Dic13 |
| Hall | C11×C13 ⋊ Dic61 |
| Sylow | C61 ⋊ Dic143 |
| Sylow | C13 ⋊ Dic671 |
| Sylow | C11 ⋊ Dic793 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D8723 |
| commutator, hypocenter | C11×C13×C61 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C11×C13×C61 | C2 |
| LCS | G ▷ C11×C13×C61 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 34892 |
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);(1,3,2,4)(6,15)(7,14)(8,13)(9,12)(10,11)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(30,89)(31,88)(32,87)(33,86)(34,85)(35,84)(36,83)(37,82)(38,81)(39,80)(40,79)(41,78)(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:
2,11,13,61,2|a^2=e,b^a=b^10,c^a=c^12,d^a=d^608726 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34892, 8);