Finite Group DatabasebetaFinite Group Databasebeta| order | 32412 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C4×#22549193 |
| Fitting, Hall | C4×C37×C73 ⋊ C3 |
| derived, Hall | C37×C73 ⋊ C3×C4 |
| Hall | C4×C73 ⋊ C37⋊C3 |
| Hall | C4×C37 ⋊ C73⋊C3 |
| Sylow | C73 ⋊ C4×C37⋊C3 |
| Sylow | C37 ⋊ C4×C73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #22549193 |
| commutator, hypocenter | C37×C73 | C3×C4 |
| Frattini | C2 | C2×#22549193 |
| Fitting | C4×C37×C73 | C3 |
| socle, cosocle | C2×C37×C73 | C2×C3 |
| prime radical | C2×#22549193 | C2 |
| LCS | G ▷ C37×C73 | |
| UCS | C1 ◁ C4 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10804 |
3612 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32412, 5);