Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C4 |
| direct product | C22×#10597386 |
| Fitting | C23×D4×C19 ⋊ C2 |
| Sylow | C19 ⋊ C22×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D19 |
| commutator, cosocle | C22×C19 | C25 |
| Frattini | C22 | C24×D19 |
| Fitting | C23×D4×C19 | C2 |
| socle | C24×C19 | C23 |
| hypercenter | C23×D4 | D19 |
| hypocenter | C19 | C22×#127 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
3000 conjugacy classes of subgroups; only the 725 normal subgroups are shown.
This group has 3000 conjugacy classes of subgroups — too many to draw. Only its 725 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1216 |
416 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #18075155, #18089074, #18089075, … |
| maximal normal subgroup of | #18075155, #18089074, #18089075, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 17781);