Finite Group DatabasebetaFinite Group Databasebeta| order | 8748 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×#72221840 |
| Fitting | C2×#14550491 ⋊ C2 |
| derived | C3×C27 ⋊ C22×C3×C9 |
| Sylow | #14550491 ⋊ C22 |
646 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
236 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221847, C2×#72221870 |
| maximal normal subgroup of | C2×#72221847, C2×#72221870 |
Past the SmallGroups library coverage — no SmallGroups id.