Finite Group DatabasebetaFinite Group Databasebeta| order | 32338 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×D437 |
| unambiguous semidirect product | C19⋊(C37×D23) |
| unambiguous semidirect product | C23⋊(C37×D19) |
| Fitting, socle, Hall | C19×C23×C37 ⋊ C2 |
| derived, Hall | C19×C23 ⋊ C2×C37 |
| Hall | C23×C37 ⋊ D19 |
| Hall | C19×C37 ⋊ D23 |
| Sylow | C23 ⋊ C37×D19 |
| Sylow | C19 ⋊ C37×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | D437 |
| commutator, cosocle, hypocenter | C19×C23 | C2×C37 |
| Frattini | C1 | G |
| Fitting, socle | C19×C23×C37 | C2 |
| LCS | G ▷ C19×C23 | |
| UCS | C1 ◁ C37 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16169 |
8140 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32338, 7);