Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C25×C32 |
| direct product | A4×#88907 |
| Sylow | C26 ⋊ C3×3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×A4×C22⋊A4 |
| commutator, socle, cosocle | C26×C3 | C33 |
| Fitting | C26×C32 | C32 |
| prime radical | C24×C32×A4 | C3 |
| hypercenter | C32 | A4×C22⋊A4 |
| hypocenter | C26 | C3×3−1+2 |
| LCS | G ▷ C26×C3 ▷ C26 | |
| UCS | C1 ◁ C3 ◁ C32 | |
3608 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 3608 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#13049240 |
| maximal normal subgroup of | A4×#13049240 |
Past the SmallGroups library coverage — no SmallGroups id.