Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C32×C4 |
| direct product | C22×#1572 |
| Fitting, socle | C22×C34 ⋊ C42 |
| derived, Sylow | C34 ⋊ C22×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #1572 |
| commutator, hypocenter | C34 | C22×C42 |
| Frattini | C1 | G |
| Fitting, socle | C22×C34 | C42 |
| prime radical | C22×C3⋊D32 | C22 |
| cosocle | C3⋊D32 | C24 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C22 | |
2636 conjugacy classes of subgroups; only the 308 normal subgroups are shown.
This group has 2636 conjugacy classes of subgroups — too many to draw. Only its 308 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72213199, C22×#72213247, C22×#72213277 |
| maximal normal subgroup of | C22×#72213199, C22×#72213247, C22×#72213277 |
Past the SmallGroups library coverage — no SmallGroups id.