Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#10597183 |
| Fitting | C3×C4×C52 ⋊ C2×C4 |
| derived, Hall | C3×C52 ⋊ C2×C42 |
| Sylow | C52 ⋊ C42×D3 |
| Sylow | C3 ⋊ C4×D5⋊AGL(1,𝔽5) |
492 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #72230650, C4×D3×D5⋊AGL(1,𝔽5), #72230672, … |
| maximal normal subgroup of | #72230650, C4×D3×D5⋊AGL(1,𝔽5), #72230672, … |
Past the SmallGroups library coverage — no SmallGroups id.