Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×#13048081 |
| Sylow | C26 ⋊ C9⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C32 | A42 |
| commutator | C24×C3 | C22×C3×C9 |
| Frattini | C32 | C22×A42 |
| Fitting, socle, prime radical | C26×C32 | C32 |
| cosocle | C24×C32 | C22×C32 |
| hypocenter | C24 | C22×C9⋊C9 |
| LCS | G ▷ C24×C3 ▷ C24 | |
| UCS | C1 ◁ C22×C32 | |
2898 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 2898 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 324 |
384 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×#72220143 |
| maximal normal subgroup of | C22×#72220143 |
Past the SmallGroups library coverage — no SmallGroups id.