Finite Group DatabasebetaFinite Group Databasebeta| order | 32412 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×(C73⋊C3)⋊D37 |
| unambiguous semidirect product | (C2×C73⋊C3)⋊D37 |
| Fitting, socle | C2×C37×C73 ⋊ C2×C3 |
| derived, Hall | C37×C73 ⋊ C22×C3 |
| Hall | C2×D2701 ⋊ C3 |
| Hall | C37×C73⋊C3 ⋊ C22 |
| Hall | C73⋊C3 ⋊ C2×D37 |
| Sylow | C73 ⋊ C2×C3×D37 |
| Sylow | C37 ⋊ C2×D73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C73⋊C3)⋊D37 |
| commutator, cosocle, hypocenter | C37×C73 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C37×C73 | C2×C3 |
| LCS | G ▷ C37×C73 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5402 |
1008 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32412, 64);