Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | GL(2,𝔽3)×AGL(1,ℤ/9) |
| Fitting | Q8×3−1+2 ⋊ C2×D3 |
| derived | C9×SL(2,𝔽3) ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | S4×AGL(1,ℤ/9) |
| commutator, cosocle, hypocenter | C9×SL(2,𝔽3) | C22×C3 |
| Frattini, socle | C2×C3 | C3×D3×S4 |
| Fitting | Q8×3−1+2 | C2×D3 |
| LCS | G ▷ C9×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 | |
377 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 377 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
80 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/9)×#5935 |
| automorphism group of | C32×D9 |
Past the SmallGroups library coverage — no SmallGroups id.