Finite Group DatabasebetaFinite Group Databasebeta| order | 2880 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | AGL(1,𝔽5)×D32⋊C4 |
| Hall | C32×C5 ⋊ C4×C22⋊C4 |
| Sylow | C32 ⋊ C22⋊C4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×D32⋊C4 |
860 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 860 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#64241 |
| maximal normal subgroup of | AGL(1,𝔽5)×#64241 |
Past the SmallGroups library coverage — no SmallGroups id.