Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#10624709⋊C2 |
| Fitting | C2×#10624709 ⋊ C2 |
| derived | C3×C27 ⋊ C22×C9 |
| Sylow | #10624709 ⋊ C22 |
239 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 239 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221820, C2×#72221842, C2×#72221843, … |
| maximal normal subgroup of | C2×#72221820, C2×#72221842, C2×#72221843, … |
Past the SmallGroups library coverage — no SmallGroups id.