Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C23×C36 |
| direct product | C3×A43 |
| Fitting, socle | C26×C3 ⋊ C33 |
| derived, Sylow | C26 ⋊ C34 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | A43 |
| commutator, cosocle, hypocenter | C26 | C34 |
| Frattini | C1 | G |
| Fitting, socle | C26×C3 | C33 |
| LCS | G ▷ C26 | |
| UCS | C1 ◁ C3 | |
2806 conjugacy classes of subgroups; only the 316 normal subgroups are shown.
This group has 2806 conjugacy classes of subgroups — too many to draw. Only its 316 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 quotient of | A4×#13049240 |
Past the SmallGroups library coverage — no SmallGroups id.