Finite Group DatabasebetaFinite Group Databasebeta| order | 3232 |
| isoclinism | isoclinic class of D101 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C24×D101 |
| unambiguous semidirect product | C101⋊C25 |
| unambiguous semidirect product | (C2×C101)⋊C24 |
| Fitting, socle | C24×C101 ⋊ C2 |
| derived, Sylow | C101 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D101 |
| commutator, cosocle, hypocenter | C101 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C24×C101 | C2 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C24 | |
748 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1616 |
832 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3232, 195);