Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C7 |
| direct product | C11⋊C5×#10596885 |
| unambiguous semidirect product | (C11×#10596885)⋊C5 |
| Fitting, socle, Hall | C72×C11 ⋊ C5×Dic3 |
| derived, Hall | C11×#3862 ⋊ C4×C5 |
| Hall | C11⋊C5×#3862 ⋊ C4 |
| Hall | C11×#10596885 ⋊ C5 |
| Hall | C72×C11⋊C5 ⋊ Dic3 |
| Hall | #3862 ⋊ C4×C11⋊C5 |
| Sylow | C72 ⋊ Dic3×C11⋊C5 |
| Sylow | C11 ⋊ C5×#10596885 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C11×#3862 | C4×C5 |
| Fitting, socle | C72×C11 | C5×Dic3 |
| prime radical | C11⋊C5×#64425 | C2 |
| cosocle | C11×#64425 | C2×C5 |
| LCS | G ▷ C11×#3862 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 154 |
70 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 244);