Finite Group DatabasebetaFinite Group Databasebeta| order | 32204 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C83 · Schur multiplier (H2) = C1 |
| direct product | C83×#87604 |
| Fitting, socle, Hall | C83×C97 ⋊ C4 |
| derived, Sylow | C97 ⋊ C4×C83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C83 | #87604 |
| commutator, hypocenter | C97 | C4×C83 |
| Frattini | C1 | G |
| Fitting, socle | C83×C97 | C4 |
| prime radical | C83×D97 | C2 |
| cosocle | D97 | C2×C83 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C83 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8051 |
2324 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32204, 6);