Finite Group DatabasebetaFinite Group Databasebeta| order | 34892 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#15691760 |
| Fitting, socle, derived, Hall | C11×C13×C61 ⋊ C4 |
| Hall | C13×C61 ⋊ Dic11 |
| Hall | C11×C61 ⋊ #261 |
| Hall | C11×C13 ⋊ Dic61 |
| Sylow | C61 ⋊ C11⋊#261 |
| Sylow | C13 ⋊ Dic671 |
| Sylow | C11 ⋊ #15691760 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C13×C61 | C4 |
| prime radical, cosocle | C11×D13×C61 | C2 |
| LCS | G ▷ C11×C13×C61 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8723 |
Polycyclic presentation:
2^2,11,13,61|a^2=b,c^a=c^10,d^a=d^5,e^a=e^60,d^b=d^122687 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34892, 22);