Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C3×D5⋊(C22⋊AGL(1,𝔽5)) |
| Fitting | C22×C3×C52 ⋊ C2×C4 |
| Hall | C3×C52 ⋊ C2×C22⋊C4 |
| Sylow | C52 ⋊ C2×C3×C22⋊C4 |
596 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D4×D5⋊AGL(1,𝔽5), C3×#13107590, C3×#13107569, … |
| maximal normal subgroup of | C3×D4×D5⋊AGL(1,𝔽5), C3×#13107590, C3×#13107569, … |
Past the SmallGroups library coverage — no SmallGroups id.