Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×D3×#379⋊C3 |
| Fitting | C2×C3×#379 ⋊ C2×C3 |
| derived | C24×C3 ⋊ C22×C3×C4 |
11482 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 11482 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#72991, C2×D3×#1020⋊C4, C2×D3×AΣL(1,𝔽64) |
| maximal normal subgroup of | C2×D3×#72991, C2×D3×#1020⋊C4, C2×D3×AΣL(1,𝔽64) |
Past the SmallGroups library coverage — no SmallGroups id.