Finite Group DatabasebetaFinite Group Databasebeta| order | 5120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C42 |
| direct product | C22×#17309⋊C5 |
| Fitting, Sylow | C22×#17309 ⋊ C5 |
| derived | #17309 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #17309⋊C5 |
| commutator, cosocle, hypocenter | #17309 | C22×C5 |
| Frattini | C24 | C22×C24⋊C5 |
| Fitting | C22×#17309 | C5 |
| socle | C26 | C24⋊C5 |
| LCS | G ▷ #17309 | |
| UCS | C1 ◁ C22 | |
9412 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 9412 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72209706, C2×#72210082 |
| maximal normal subgroup of | C22×#72209706, C2×#72210082 |
Past the SmallGroups library coverage — no SmallGroups id.