Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×((C3⋊S4)⋊A4)⋊C2 |
| derived | (C3×A4)⋊A4 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | ((C3⋊S4)⋊A4)⋊C2 |
| commutator, cosocle, hypocenter | (C3×A4)⋊A4 | C22×C3 |
| Frattini | C3 | C3×S42 |
| Fitting, socle | C24×C32 | D32 |
| LCS | G ▷ (C3×A4)⋊A4 | |
| UCS | C1 ◁ C3 | |
1275 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 1275 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.
105 conjugacy classes — view the full character table.
| maximal subgroup of | #72222957 |
Past the SmallGroups library coverage — no SmallGroups id.