Finite Group DatabasebetaFinite Group Databasebeta| order | 32204 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C83⋊#87604 |
| Fitting, socle, derived, Hall | C83×C97 ⋊ C4 |
| Sylow | C97 ⋊ Dic83 |
| Sylow | C83 ⋊ #87604 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C83×C97 | C4 |
| prime radical, cosocle | C83×D97 | C2 |
| LCS | G ▷ C83×C97 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8051 |
Polycyclic presentation:
2^2,83,97|a^2=b,c^a=c^82,d^a=d^75,d^b=d^962078 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32204, 7);