Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C212 |
| direct product | C22×#85493 |
| Fitting | C25×D4 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×S4 |
| commutator, cosocle | C22×A4 | C25 |
| Frattini | C22 | C24×S4 |
| Fitting | C25×D4 | D3 |
| socle | C26 | C22×D3 |
| hypercenter | C23×D4 | S4 |
| hypocenter | A4 | C22×#120 |
| LCS | G ▷ C22×A4 ▷ A4 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
44363 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | #72259267 |
| maximal normal subgroup of | #72259267 |
Past the SmallGroups library coverage — no SmallGroups id.