Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C211 |
| direct product | C22×D8×S4 |
| 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 | C23×D8 |
| LCS | G ▷ C4×A4 ▷ C2×A4 ▷ A4 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×D8 | |
14275 conjugacy classes of subgroups; only the 654 normal subgroups are shown.
This group has 14275 conjugacy classes of subgroups — too many to draw. Only its 654 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72240991, C22×S4×AGL(1,ℤ/8) |
| maximal normal subgroup of | C22×S4×AGL(1,ℤ/8) |
Past the SmallGroups library coverage — no SmallGroups id.