Finite Group DatabasebetaFinite Group Databasebeta| order | 2880 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C3×C4 |
| direct product | AGL(1,𝔽5)×#3757 |
| Hall | C32×C5 ⋊ C4×C22⋊C4 |
| Sylow | C32 ⋊ C22⋊C4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×#3757 |
1548 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#64146, C22⋊C4×C3⋊D3×AGL(1,𝔽5), AGL(1,𝔽5)×#64162 |
| maximal normal subgroup of | AGL(1,𝔽5)×#64146, C22⋊C4×C3⋊D3×AGL(1,𝔽5), AGL(1,𝔽5)×#64162 |
Past the SmallGroups library coverage — no SmallGroups id.