Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C28 |
| direct product | C2×A4×B(4,𝔽2) |
| Fitting, Sylow | C23×B(4,𝔽2) ⋊ C3 |
12720 conjugacy classes of subgroups; only the 324 normal subgroups are shown.
This group has 12720 conjugacy classes of subgroups — too many to draw. Only its 324 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | C2×S4×B(4,𝔽2) |
| maximal normal subgroup of | C2×S4×B(4,𝔽2) |
Past the SmallGroups library coverage — no SmallGroups id.