Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C2×D3×((C22⋊C9)⋊C2)⋊C3 |
| derived | C3×C22⋊C9 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×((C22⋊C9)⋊C2)⋊C3 |
| commutator, cosocle, hypocenter | C3×C22⋊C9 | C23×C3 |
| Frattini | C3 | C2×C3×D3×S4 |
| Fitting | C23×C33 | C2×D3 |
| socle | C23×C32 | C2×C3×D3 |
| LCS | G ▷ C3×C22⋊C9 | |
| UCS | C1 ◁ C2 | |
1116 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
114 conjugacy classes — view the full character table.
| maximal subgroup of | #67×((C22⋊C9)⋊C2)⋊C3 |
| maximal normal subgroup of | #67×((C22⋊C9)⋊C2)⋊C3 |
| maximal quotient of | #67×((C22⋊C9)⋊C2)⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.