Finite Group DatabasebetaFinite Group Databasebeta| order | 32308 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×#11716161 |
| Fitting, socle, Hall | C41×C197 ⋊ C4 |
| derived, Sylow | C197 ⋊ C4×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | #11716161 |
| commutator, hypocenter | C197 | C4×C41 |
| Frattini | C1 | G |
| Fitting, socle | C41×C197 | C4 |
| prime radical | C41×D197 | C2 |
| cosocle | D197 | C2×C41 |
| LCS | G ▷ C197 | |
| UCS | C1 ◁ C41 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8077 |
2173 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32308, 6);