Finite Group DatabasebetaFinite Group Databasebeta| order | 34276 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic8569 |
| unambiguous semidirect product | C11⋊Dic779 |
| unambiguous semidirect product | C19⋊Dic451 |
| derived, Hall | C11×C19×C41 ⋊ C4 |
| Hall | C19×C41 ⋊ Dic11 |
| Hall | C11×C41 ⋊ Dic19 |
| Hall | C11×C19 ⋊ Dic41 |
| Sylow | C41 ⋊ Dic209 |
| Sylow | C19 ⋊ Dic451 |
| Sylow | C11 ⋊ Dic779 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D8569 |
| commutator, hypocenter | C11×C19×C41 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C11×C19×C41 | C2 |
| LCS | G ▷ C11×C19×C41 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 34276 |
A minimal faithful permutation representation — 2 generators on 75 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);(1,3,2,4)(6,15)(7,14)(8,13)(9,12)(10,11)(17,34)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)(36,75)(37,74)(38,73)(39,72)(40,71)(41,70)(42,69)(43,68)(44,67)(45,66)(46,65)(47,64)(48,63)(49,62)(50,61)(51,60)(52,59)(53,58)(54,57)(55,56)Polycyclic presentation:
2,11,19,41,2|a^2=e,b^a=b^10,c^a=c^18,d^a=d^408572 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34276, 8);