Finite Group DatabasebetaFinite Group Databasebeta| order | 32412 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×#64408⋊C3 |
| unambiguous semidirect product | #64408⋊(C3×C37) |
| Fitting, socle, Hall | C37×C73 ⋊ C3×C4 |
| derived, Sylow | C73 ⋊ C3×C4×C37 |
| Hall | C37×#64408 ⋊ C3 |
| Hall | C37×C73⋊C3 ⋊ C4 |
| Hall | #64408 ⋊ C3×C37 |
| Hall | C73⋊C3 ⋊ C4×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | #64408⋊C3 |
| commutator, hypocenter | C73 | C3×C4×C37 |
| Frattini | C1 | G |
| Fitting, socle | C37×C73 | C3×C4 |
| prime radical | C37×D73⋊C3 | C2 |
| cosocle | D73 | C2×C3×C37 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C37 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2701 |
666 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32412, 26);