Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| isoclinism | isoclinic class of #64516 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C23×D152 |
| Fitting | C23×C8×C19 ⋊ C2 |
| Sylow | C19 ⋊ C23×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | D76 |
| commutator, cosocle | C4×C19 | C25 |
| Frattini | C4 | C24×D19 |
| Fitting | C23×C8×C19 | C2 |
| socle | C24×C19 | D4 |
| hypercenter | C23×C8 | D19 |
| hypocenter | C19 | C23×D8 |
| LCS | G ▷ C4×C19 ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×C8 | |
1976 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
632 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #18089337, #18089339, #18089363, … |
| maximal normal subgroup of | #18089337, #18089339, #18089363, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 19226);