Finite Group DatabasebetaFinite Group Databasebeta| order | 7200 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#72229619 |
| Hall | C32×C52 ⋊ C2×C4⋊C4 |
| Sylow | C52 ⋊ C2×#3750 |
| Sylow | C32 ⋊ C2×C4⋊#1043 |
2208 conjugacy classes of subgroups; only the 364 normal subgroups are shown.
This group has 2208 conjugacy classes of subgroups — too many to draw. Only its 364 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1800 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3⋊D3×C4⋊#1043, C2×#638×#1043, C2×#72230625 |
| maximal normal subgroup of | C2×C3⋊D3×C4⋊#1043, C2×#638×#1043, C2×#72230625 |
Past the SmallGroups library coverage — no SmallGroups id.