Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C3×#11717039 |
| Fitting | C2×C3×C4×C52 ⋊ C22 |
| Hall | C3×C52 ⋊ C2×C22⋊C4 |
| Sylow | C52 ⋊ C2×C3×C22⋊C4 |
636 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#13104045, D3×#11717039, #72260189 |
| maximal normal subgroup of | C3×#13104045, D3×#11717039, #72260189 |
| maximal quotient of | C3×#13100574 |
Past the SmallGroups library coverage — no SmallGroups id.