Finite Group DatabasebetaFinite Group Databasebeta| order | 3232 |
| isoclinism | isoclinic class of #87938 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C23×#87938 |
| unambiguous semidirect product | D101⋊(C22×C4) |
| Fitting, socle | C23×C101 ⋊ C4 |
| derived, Sylow | C101 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #87938 |
| commutator, hypocenter | C101 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C101 | C4 |
| prime radical | C23×D101 | C2 |
| cosocle | D101 | C24 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C23 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 808 |
232 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3232, 235);