Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
| direct product | #41×#1020 |
| Fitting | C24×#41 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×#1020 |
| commutator, cosocle | C2×C22⋊A4 | C24 |
| Frattini | C2 | C23×#1020 |
| Fitting | C24×#41 | D3 |
| socle | C25 | C23×D3 |
| hypercenter | #41 | #1020 |
| hypocenter | C22⋊A4 | C2×#41 |
| LCS | G ▷ C2×C22⋊A4 ▷ C22⋊A4 | |
| UCS | C1 ◁ C4 ◁ #41 | |
14100 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 14100 conjugacy classes of subgroups — too many to draw. Only its 155 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/8)×#1020, #41×A4⋊S4, #41×#1020⋊C2 |
| maximal normal subgroup of | AGL(1,ℤ/8)×#1020, #41×#1020⋊C2 |
| maximal quotient of | C4×D4×#1020 |
Past the SmallGroups library coverage — no SmallGroups id.