Finite Group DatabasebetaFinite Group Databasebeta| order | 32412 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C37×C73 ⋊ C3×C4 |
| Hall | Dic2701 ⋊ C3 |
| Hall | C37×C73⋊C3 ⋊ C4 |
| Hall | C73⋊C3 ⋊ Dic37 |
| Sylow | C73 ⋊ C3×Dic37 |
| Sylow | C37 ⋊ Dic73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C73⋊C3)⋊D37 |
| commutator, hypocenter | C37×C73 | C3×C4 |
| Fitting, socle, cosocle | C2×C37×C73 | C2×C3 |
| prime radical | C2×C37×C73⋊C3 | C2 |
| LCS | G ▷ C37×C73 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10804 |
Polycyclic presentation:
2,3,37,73,2|a^2=e,c^a=c^36,d^a=d^72,d^b=d^81008 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32412, 21);