Finite Group DatabasebetaFinite Group Databasebeta| order | 2880 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#13088746 |
| Fitting | C23×C32×C5 ⋊ C2×C4 |
| Hall | C32×C5 ⋊ C22×C22⋊C4 |
| Sylow | C32 ⋊ C22×C22⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×#63974 |
3444 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×#3811, C2×#72231569, #72260215, … |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×#3811, #72260215, #72260246 |
| maximal quotient of | #72230450, C2×#72231569 |
Past the SmallGroups library coverage — no SmallGroups id.