Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C7 |
| direct product | C5×C11×#10596885 |
| Fitting, socle, Hall | C5×C72×C11 ⋊ Dic3 |
| derived, Hall | #3862 ⋊ C4×C5×C11 |
| Hall | C5×C11×#3862 ⋊ C4 |
| Hall | C11×#3862 ⋊ C4×C5 |
| Hall | C5×#3862 ⋊ C4×C11 |
| Hall | C72×C11 ⋊ C5×Dic3 |
| Hall | C5×C72 ⋊ C11×Dic3 |
| Sylow | C72 ⋊ C5×C11×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C11 | #10596885 |
| commutator, hypocenter | #3862 | C4×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C11 | Dic3 |
| prime radical | C5×C11×#64425 | C2 |
| cosocle | #64425 | C2×C5×C11 |
| LCS | G ▷ #3862 | |
| UCS | C1 ◁ C5×C11 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 770 |
550 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 321);