Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×Dic165 |
| unambiguous semidirect product | C3⋊(C72×Dic55) |
| unambiguous semidirect product | C11⋊(C72×Dic15) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C72 | D165 |
| commutator, hypocenter | C3×C5×C11 | C4×C72 |
| Frattini | C2 | C72×D165 |
| Fitting, socle, prime radical | C2×C3×C5×C72×C11 | C2 |
| cosocle | C2×C3×C5×C11 | C2×C72 |
| LCS | G ▷ C3×C5×C11 | |
| UCS | C1 ◁ C2×C72 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32340 |
8232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 222);