Finite Group DatabasebetaFinite Group Databasebeta| order | 32332 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×#10587739 |
| Fitting, socle, Hall | C59×C137 ⋊ C4 |
| derived, Sylow | C137 ⋊ C4×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C59 | #10587739 |
| commutator, hypocenter | C137 | C4×C59 |
| Frattini | C1 | G |
| Fitting, socle | C59×C137 | C4 |
| prime radical | C59×D137 | C2 |
| cosocle | D137 | C2×C59 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C59 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8083 |
2242 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32332, 6);