Finite Group DatabasebetaFinite Group Databasebeta| order | 32412 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #30633764⋊C2 |
| unambiguous semidirect product | #30633768⋊C2 |
| unambiguous semidirect product | #30633772⋊C2 |
| Fitting, socle, derived, Hall | C37×C73 ⋊ C22×C3 |
| Hall | D37×D73 ⋊ C3 |
| Hall | #22549194 ⋊ C22 |
| Sylow | C73 ⋊ C2×D37⋊C3 |
| Sylow | C37 ⋊ C2×D73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C37×C73 | C22×C3 |
| LCS | G ▷ C37×C73 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2701 |
Polycyclic presentation:
2^2,3,37,73|e^a=e^72,d^b=d^36,d^c=d^26,e^c=e^8264 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32412, 41);