Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C23 |
| direct product | S4×#6258 |
| Fitting | C24×C32 ⋊ D32 |
| derived | A4×C22⋊H(3,𝔽3) ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | S4×C3⋊S4 |
| commutator, cosocle, hypocenter | A4×C22⋊H(3,𝔽3) | C22 |
| Fitting | C24×C32 | D32 |
| socle | C24×C3 | D3×C3⋊D3 |
| LCS | G ▷ A4×C22⋊H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
1468 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 1468 conjugacy classes of subgroups — too many to draw. Only its 45 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 | #72222957 |
Past the SmallGroups library coverage — no SmallGroups id.