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 | #24925161 ⋊ C3 |
| Hall | C37×C73⋊C3 ⋊ C4 |
| Hall | C73⋊C3 ⋊ Dic37 |
| Sylow | C73 ⋊ C3×Dic37 |
| Sylow | C37 ⋊ #64408⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37×C73 | C3×C4 |
| prime radical | C37×D73⋊C3 | C2 |
| cosocle | C37×D73 | 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^36,e^a=e^27,e^b=e^8,e^c=e^72342 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32412, 52);