Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | S4×(C3⋊S4)⋊C3 |
| Fitting | C24×C32 ⋊ D32 |
| derived | C3×A42 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×A42 | C22×C3 |
| Frattini | C3 | C3×S42 |
| Fitting | C24×C32 | D32 |
| socle | C24×C3 | C3×D32 |
| LCS | G ▷ C3×A42 | |
| UCS | C1 | |
1194 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 1194 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
95 conjugacy classes — view the full character table.
| maximal subgroup of | S4×((C3⋊S4)⋊C3)⋊C2 |
| maximal normal subgroup of | S4×((C3⋊S4)⋊C3)⋊C2 |
| maximal quotient of | #72222968 |
Past the SmallGroups library coverage — no SmallGroups id.