Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | #41×GL(2,ℤ/4) |
| Fitting | C24×#41 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×S4 |
| commutator, cosocle | C22×A4 | C25 |
| Frattini | C22 | C24×S4 |
| Fitting | C24×#41 | D3 |
| socle | C24 | C24×D3 |
| hypercenter | C22×#41 | S4 |
| hypocenter | A4 | D4×#41 |
| LCS | G ▷ C22×A4 ▷ A4 | |
| UCS | C1 ◁ C2×C4 ◁ C22×#41 | |
15568 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/8)×GL(2,ℤ/4), #41×A4⋊S4 |
| maximal normal subgroup of | AGL(1,ℤ/8)×GL(2,ℤ/4) |
Past the SmallGroups library coverage — no SmallGroups id.