Finite Group DatabasebetaFinite Group Databasebeta| order | 32412 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊#22549193 |
| Fitting, socle, derived, Hall | C22×C37×C73 ⋊ C3 |
| Hall | C37×C73 ⋊ A4 |
| Hall | C22×C73 ⋊ C37⋊C3 |
| Hall | C22×C37 ⋊ C73⋊C3 |
| Sylow | C73 ⋊ C22⋊(C37⋊C3) |
| Sylow | C37 ⋊ C22⋊(C73⋊C3) |
| Sylow | C22 ⋊ #22549193 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C37×C73 | C3 |
| LCS | G ▷ C22×C37×C73 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10804 |
Polycyclic presentation:
3,2^2,37,73|b^a=c,c^a=bc,d^a=d^26,e^a=e^643604 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32412, 89);