Finite Group DatabasebetaFinite Group Databasebeta| order | 32868 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×Dic913 |
| unambiguous semidirect product | C11⋊(C32×Dic83) |
| unambiguous semidirect product | C83⋊(C32×Dic11) |
| derived, Hall | C11×C83 ⋊ C32×C4 |
| Hall | C32×C11×C83 ⋊ C4 |
| Hall | C32×C83 ⋊ Dic11 |
| Hall | C32×C11 ⋊ Dic83 |
| Sylow | C83 ⋊ C32×Dic11 |
| Sylow | C11 ⋊ C32×Dic83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D913 |
| commutator, hypocenter | C11×C83 | C32×C4 |
| Frattini | C2 | C32×D913 |
| Fitting, socle, prime radical | C2×C32×C11×C83 | C2 |
| cosocle | C2×C11×C83 | C2×C32 |
| LCS | G ▷ C11×C83 | |
| UCS | C1 ◁ C2×C32 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32868 |
8244 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32868, 34);