Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C23 |
| direct product | D9×#5935 |
| Fitting | C9×H(5,𝔽2) ⋊ C2×D3 |
| derived | C9×#997 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9×#1020 |
| commutator, cosocle, hypocenter | C9×#997 | C22 |
| Frattini, socle | C2×C3 | D3×#1020 |
| Fitting | C9×H(5,𝔽2) | C2×D3 |
| LCS | G ▷ C9×#997 | |
| UCS | C1 ◁ C2 | |
1035 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 1035 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
78 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/9)×#5935 |
| maximal normal subgroup of | AGL(1,ℤ/9)×#5935 |
Past the SmallGroups library coverage — no SmallGroups id.