Finite Group DatabasebetaFinite Group Databasebeta| order | 7200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C2×C3⋊Dic3×#1043 |
| derived, Hall | C32×C52 ⋊ C2×C42 |
| Sylow | C52 ⋊ C2×C4×C3⋊Dic3 |
| Sylow | C32 ⋊ C2×C4×#1043 |
2592 conjugacy classes of subgroups; only the 420 normal subgroups are shown.
This group has 2592 conjugacy classes of subgroups — too many to draw. Only its 420 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1800 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4×C3⋊D3×#1043, C2×#638×#1043, C2×#72230625 |
| maximal normal subgroup of | C2×C4×C3⋊D3×#1043, C2×#638×#1043, C2×#72230625 |
Past the SmallGroups library coverage — no SmallGroups id.