Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×#11927256 |
| Fitting | C2×C19×#124 ⋊ C2 |
| Sylow | C19 ⋊ C2×#555 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D19 |
| commutator, cosocle | C22×C19 | C25 |
| Frattini | C22 | C24×D19 |
| Fitting | C2×C19×#124 | C2 |
| socle | C23×C19 | C24 |
| hypercenter | C2×#124 | D19 |
| hypocenter | C19 | C2×#555 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C2×#124 | |
1240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
302 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 18047);