Finite Group DatabasebetaFinite Group Databasebeta| order | 32164 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×D17×D43 |
| unambiguous semidirect product | (D17×C43)⋊(C2×C11) |
| unambiguous semidirect product | (C17×D43)⋊(C2×C11) |
| unambiguous semidirect product | D731⋊(C2×C11) |
| Fitting, socle, Hall | C11×C17×C43 ⋊ C22 |
| derived, Hall | C17×C43 ⋊ C22×C11 |
| Hall | C11×C43 ⋊ C2×D17 |
| Hall | C11×C17 ⋊ C2×D43 |
| Sylow | C43 ⋊ C2×C11×D17 |
| Sylow | C17 ⋊ C2×C11×D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D17×D43 |
| commutator, cosocle, hypocenter | C17×C43 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C17×C43 | C22 |
| LCS | G ▷ C17×C43 | |
| UCS | C1 ◁ C11 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8041 |
2530 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32164, 12);