Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C27 |
| direct product | C4×#87588 |
| Fitting | C26×C4 ⋊ D3 |
| derived | C22⋊(C22⋊A4) ⋊ C2×C4 |
13133 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 13133 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#87588, C4×#87588⋊C2, C4×#87588⋊C3, … |
| maximal normal subgroup of | C4×#87588⋊C2, C4×#87588⋊C3, C2×C4×#87588 |
| maximal quotient of | C4×#11715850, AGL(1,𝔽5)×#87588, #72342887, … |
Past the SmallGroups library coverage — no SmallGroups id.