Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22×C32 |
| direct product | C3×(C3⋊S4)⋊A4 |
| derived | C22×C3×A4 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C3⋊S4)⋊A4 |
| commutator, cosocle, hypocenter | C22×C3×A4 | C2×C32 |
| Frattini | C3 | C3×A4×S4 |
| Fitting, socle | C24×C32 | C3×D3 |
| LCS | G ▷ C22×C3×A4 | |
| UCS | C1 ◁ C3 | |
545 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 545 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
84 conjugacy classes — view the full character table.
| maximal subgroup of | #72220526, #72220531, C3×((C3⋊S4)⋊A4)⋊C2 |
| maximal normal subgroup of | #72220526, C3×((C3⋊S4)⋊A4)⋊C2 |
Past the SmallGroups library coverage — no SmallGroups id.