Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D5×(C2×D3)⋊AGL(1,𝔽5) |
| Hall | C3×C52 ⋊ C2×C22⋊C4 |
| Sylow | C52 ⋊ C2×(C2×D3)⋊C4 |
| Sylow | C3 ⋊ D5×C22⋊AGL(1,𝔽5) |
560 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 92 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 | #72229979, D3×D5×C22⋊AGL(1,𝔽5), #72230201 |
| maximal normal subgroup of | #72229979, D3×D5×C22⋊AGL(1,𝔽5), #72230201 |
Past the SmallGroups library coverage — no SmallGroups id.