Finite Group DatabasebetaFinite Group Databasebeta| order | 32204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C83 · Schur multiplier (H2) = C2 |
| direct product | C2×C83×D97 |
| unambiguous semidirect product | C97⋊(C22×C83) |
| unambiguous semidirect product | (C2×C97)⋊(C2×C83) |
| Fitting, socle | C2×C83×C97 ⋊ C2 |
| derived, Sylow | C97 ⋊ C22×C83 |
| Hall | C83×C97 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C83 | D97 |
| commutator, cosocle, hypocenter | C97 | C22×C83 |
| Frattini | C1 | G |
| Fitting, socle | C2×C83×C97 | C2 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C2×C83 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16102 |
8300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32204, 9);