Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C23×C33 |
| direct product | A4×(C22⋊A4)⋊C9 |
| derived, Sylow | C26 ⋊ C32×C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | A43 |
| commutator, hypocenter | C26 | C32×C9 |
| Fitting, socle, cosocle | C26×C3 | C33 |
| prime radical | C3×A4×C22⋊A4 | C3 |
| LCS | G ▷ C26 | |
| UCS | C1 ◁ C3 | |
1027 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 1027 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#13049240, A4×#11724027 |
| maximal normal subgroup of | A4×#13049240, A4×#11724027 |
Past the SmallGroups library coverage — no SmallGroups id.