Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C22×C33 |
| direct product | C3×C3⋊(A4⋊S4) |
| Fitting, socle | C24×C32 ⋊ C3⋊D3 |
| derived | C3×A42 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(A4⋊S4) |
| commutator, cosocle, hypocenter | C3×A42 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C24×C32 | C3⋊D3 |
| LCS | G ▷ C3×A42 | |
| UCS | C1 ◁ C3 | |
1065 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 1065 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
90 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×A4⋊S4, D3×C3⋊(A4⋊S4), #72220734, … |
| maximal normal subgroup of | C3×D3×A4⋊S4, D3×C3⋊(A4⋊S4), #72220734, … |
Past the SmallGroups library coverage — no SmallGroups id.