Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C22×#85457 |
| Fitting | C24×D8 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×S4 |
| commutator, cosocle | C4×A4 | C25 |
| Frattini | C4 | C24×S4 |
| Fitting | C24×D8 | D3 |
| socle | C25 | D3×D4 |
| hypercenter | C22×D8 | S4 |
| hypocenter | A4 | C22×AGL(1,ℤ/8) |
| LCS | G ▷ C4×A4 ▷ C2×A4 ▷ A4 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×D8 | |
12539 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72240992, C22×S4×AGL(1,ℤ/8) |
| maximal normal subgroup of | C22×S4×AGL(1,ℤ/8) |
Past the SmallGroups library coverage — no SmallGroups id.