Finite Group DatabasebetaFinite Group Databasebeta| order | 2880 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25×C3 |
| direct product | C3⋊D3×(C2×AGL(1,𝔽5))⋊C4 |
| Fitting | C2×C32×C4×C5 ⋊ C2×C4 |
| Hall | C32×C5 ⋊ C2×#95 |
| Sylow | C32 ⋊ C2×(C2×AGL(1,𝔽5))⋊C4 |
| Sylow | C5 ⋊ C3⋊D3×#95 |
1980 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊C4×C3⋊D3×AGL(1,𝔽5), C3⋊D3×#65779, C3⋊D3×#65699 |
| maximal normal subgroup of | C22⋊C4×C3⋊D3×AGL(1,𝔽5), C3⋊D3×#65779, C3⋊D3×#65699 |
Past the SmallGroups library coverage — no SmallGroups id.