Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | #3861×Dic55 |
| unambiguous semidirect product | C11⋊(Dic5×#3861) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D55×#3861 |
| commutator, hypocenter | C5×C72×C11 | C3×C4 |
| Fitting, socle, cosocle | C2×C5×C72×C11 | C2×C3 |
| prime radical | C2×C5×C11×#3861 | C2 |
| LCS | G ▷ C5×C72×C11 | |
| UCS | C1 ◁ C2 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10780 |
1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 207);