Finite Group DatabasebetaFinite Group Databasebeta| order | 32332 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C137 · Schur multiplier (H2) = C1 |
| direct product | C137×Dic59 |
| unambiguous semidirect product | C59⋊(C4×C137) |
| derived, Sylow | C59 ⋊ C4×C137 |
| Hall | C59×C137 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C137 | D59 |
| commutator, hypocenter | C59 | C4×C137 |
| Frattini | C2 | D59×C137 |
| Fitting, socle, prime radical | C2×C59×C137 | C2 |
| cosocle | C2×C59 | C2×C137 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C2×C137 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32332 |
8494 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32332, 2);