Finite Group DatabasebetaFinite Group Databasebeta| order | 32412 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C37×C73 ⋊ C3×C4 |
| Hall | #24925160 ⋊ C3 |
| Hall | C73×C37⋊C3 ⋊ C4 |
| Hall | C37⋊C3 ⋊ Dic73 |
| Sylow | C73 ⋊ #3866⋊C3 |
| Sylow | C37 ⋊ C3×Dic73 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37×C73 | C3×C4 |
| prime radical | C73×D37⋊C3 | C2 |
| cosocle | C73×D37 | C2×C3 |
| LCS | G ▷ C37×C73 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2701 |
Polycyclic presentation:
2,3,2,37,73|a^2=c,d^a=d^31,e^a=e^72,d^b=d^26,d^c=d^36447 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32412, 38);