Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×#13750⋊C3 |
| Fitting, Sylow | C2×#13750 ⋊ C3 |
2423 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 2423 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #72268622, #72268676 |
| maximal normal subgroup of | #72268676 |
| maximal quotient of | C2×#72222564 |
Past the SmallGroups library coverage — no SmallGroups id.