Finite Group DatabasebetaFinite Group Databasebeta| order | 32412 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C73 · Schur multiplier (H2) = C2 |
| Fitting, socle | C2×C37×C73 ⋊ C2×C3 |
| derived, Sylow | C37 ⋊ C22×C3×C73 |
| Hall | C2×C73×D37 ⋊ C3 |
| Hall | C73×C37⋊C3 ⋊ C22 |
| Hall | C37×C73 ⋊ C22×C3 |
| Hall | C2×D37 ⋊ C3×C73 |
| Hall | C37⋊C3 ⋊ C22×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C73 | D37⋊C3 |
| commutator, cosocle, hypocenter | C37 | C22×C3×C73 |
| Frattini | C1 | G |
| Fitting, socle | C2×C37×C73 | C2×C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C73 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5402 |
1752 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32412, 55);