Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| isoclinism | isoclinic class of (C3⋊S4)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C24×C32 |
| direct product | C22×C3×(C3⋊S4)⋊C3 |
| Fitting | C24×C33 ⋊ D3 |
| derived | C3×A4 ⋊ C23×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | (C3⋊S4)⋊C3 |
| commutator, cosocle, hypocenter | C3×A4 | C23×C32 |
| Frattini | C3 | C22×C32×S4 |
| Fitting | C24×C33 | D3 |
| socle | C24×C32 | C3×D3 |
| LCS | G ▷ C3×A4 | |
| UCS | C1 ◁ C22×C3 | |
1776 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 1776 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
228 conjugacy classes — view the full character table.
| maximal subgroup of | #72220526, C22×((C3⋊S4)⋊C3)⋊D3, C3×#13164262, … |
| maximal normal subgroup of | #72220526, C22×((C3⋊S4)⋊C3)⋊D3, C3×#13164262, … |
Past the SmallGroups library coverage — no SmallGroups id.