Finite Group DatabasebetaFinite Group Databasebeta| order | 32164 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×Dic473 |
| unambiguous semidirect product | C11⋊(C17×Dic43) |
| unambiguous semidirect product | C43⋊(C17×Dic11) |
| derived, Hall | C11×C43 ⋊ C4×C17 |
| Hall | C11×C17×C43 ⋊ C4 |
| Hall | C17×C43 ⋊ Dic11 |
| Hall | C11×C17 ⋊ Dic43 |
| Sylow | C43 ⋊ C17×Dic11 |
| Sylow | C11 ⋊ C17×Dic43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | D473 |
| commutator, hypocenter | C11×C43 | C4×C17 |
| Frattini | C2 | C17×D473 |
| Fitting, socle, prime radical | C2×C11×C17×C43 | C2 |
| cosocle | C2×C11×C43 | C2×C17 |
| LCS | G ▷ C11×C43 | |
| UCS | C1 ◁ C2×C17 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32164 |
8092 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32164, 6);