Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C9 |
| direct product | D9×C9⋊D9 |
| Fitting, derived, Sylow | C93 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C93 | C22 |
| Frattini, socle | C33 | D3×C3⋊D3 |
| LCS | G ▷ C93 | |
| UCS | C1 | |
721 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 721 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#92314, AGL(1,ℤ/9)×C9⋊D9, #72243293, … |
| maximal normal subgroup of | D9×#92314, AGL(1,ℤ/9)×C9⋊D9, #72243293, … |
Past the SmallGroups library coverage — no SmallGroups id.