Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×D92 |
| Fitting, Sylow | C93 ⋊ C22 |
| derived | C92 ⋊ C22×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D92 |
| commutator, hypocenter | C92 | C22×C9 |
| Frattini, socle | C33 | C3×D32 |
| Fitting | C93 | C22 |
| prime radical | C3×D92 | C3 |
| cosocle | C3×C92 | C22×C3 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C9 | |
334 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×#92265⋊C2, D92×3−1+2, #72243318, … |
| maximal normal subgroup of | C9×#92265⋊C2, D92×3−1+2, #72243318, … |
Past the SmallGroups library coverage — no SmallGroups id.