Finite Group DatabasebetaFinite Group Databasebeta| order | 32494 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(D211⋊C7) |
| unambiguous semidirect product | (C211⋊C7)⋊D11 |
| unambiguous semidirect product | D2321⋊C7 |
| Fitting, socle, derived, Hall | C11×C211 ⋊ C2×C7 |
| Hall | C11×C211⋊C7 ⋊ C2 |
| Hall | D2321 ⋊ C7 |
| Hall | C211⋊C7 ⋊ D11 |
| Sylow | C211 ⋊ C7×D11 |
| Sylow | C11 ⋊ D211⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C211 | C2×C7 |
| LCS | G ▷ C11×C211 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2321 |
Polycyclic presentation:
2,7,11,211|c^a=c^10,d^a=d^210,d^b=d^171214 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32494, 12);