Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C216 |
| direct product | C2×D3×D4×C22⋊C4 |
| Fitting | C2×C3×D4×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ C22×D4×C22⋊C4 |
83924 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3×D4×#120, D3×#518019, D3×#4306523, … |
| maximal normal subgroup of | C2×D3×D4×#120, D3×#518019, D3×#4306523, … |
Past the SmallGroups library coverage — no SmallGroups id.