Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | A4×((C22⋊C9)⋊C2)⋊C3 |
| derived | C22×C22⋊C9 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C22×C22⋊C9 | C2×C32 |
| Frattini | C3 | C3×A4×S4 |
| Fitting | C24×C32 | C3×D3 |
| socle | C24×C3 | C32×D3 |
| LCS | G ▷ C22×C22⋊C9 | |
| UCS | C1 | |
415 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 415 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
76 conjugacy classes — view the full character table.
| maximal subgroup of | S4×((C22⋊C9)⋊C2)⋊C3, C2×A4×((C22⋊C9)⋊C2)⋊C3 |
| maximal normal subgroup of | S4×((C22⋊C9)⋊C2)⋊C3, C2×A4×((C22⋊C9)⋊C2)⋊C3 |
| maximal quotient of | #72220173, A4×#1094⋊C4, C2×A4×((C22⋊C9)⋊C2)⋊C3, … |
Past the SmallGroups library coverage — no SmallGroups id.