Finite Group DatabasebetaFinite Group Databasebeta| order | 32412 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×Dic73⋊C3 |
| unambiguous semidirect product | Dic73⋊(C3×C37) |
| derived, Sylow | C73 ⋊ C3×C4×C37 |
| Hall | C37×Dic73 ⋊ C3 |
| Hall | C37×C73⋊C3 ⋊ C4 |
| Hall | C37×C73 ⋊ C3×C4 |
| Hall | Dic73 ⋊ C3×C37 |
| Hall | C73⋊C3 ⋊ C4×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C37 | D73⋊C3 |
| commutator, hypocenter | C73 | C3×C4×C37 |
| Frattini | C2 | C37×D73⋊C3 |
| Fitting, socle | C2×C37×C73 | C2×C3 |
| prime radical | C2×C37×C73⋊C3 | C2 |
| cosocle | C2×C73 | C2×C3×C37 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C37 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10804 |
1332 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32412, 13);