Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×#997 |
| Fitting, Sylow | C2×D4×H(5,𝔽2) ⋊ C3 |
21943 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 21943 conjugacy classes of subgroups — too many to draw. Only its 211 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 64 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4×#5934, C2×D4×#5935, C2×D4×B(4,𝔽2)⋊C3, … |
| maximal normal subgroup of | C2×D4×#5934, C2×D4×#5935, C2×D4×B(4,𝔽2)⋊C3, … |
Past the SmallGroups library coverage — no SmallGroups id.