Finite Group DatabasebetaFinite Group Databasebeta| order | 32204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D83×D97 |
| unambiguous semidirect product | (C97×D83)⋊C2 |
| unambiguous semidirect product | (C83×D97)⋊C2 |
| unambiguous semidirect product | D8051⋊C2 |
| Fitting, socle, derived, Hall | C83×C97 ⋊ C22 |
| Sylow | C97 ⋊ C2×D83 |
| Sylow | C83 ⋊ C2×D97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C83×C97 | C22 |
| LCS | G ▷ C83×C97 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8051 |
2150 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32204, 8);