Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C25×C36 |
| direct product | C32×A4×C22⋊A4 |
| Fitting, socle | C26×C32 ⋊ C32 |
| derived, Sylow | C26 ⋊ C34 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | A4×C22⋊A4 |
| commutator, cosocle, hypocenter | C26 | C34 |
| Frattini | C1 | G |
| Fitting, socle | C26×C32 | C32 |
| LCS | G ▷ C26 | |
| UCS | C1 ◁ C32 | |
6584 conjugacy classes of subgroups; only the 444 normal subgroups are shown.
This group has 6584 conjugacy classes of subgroups — too many to draw. Only its 444 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 324 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | A4×#13049240, C3×A4×C3⋊#1020 |
| maximal normal subgroup of | A4×#13049240, C3×A4×C3⋊#1020 |
Past the SmallGroups library coverage — no SmallGroups id.