Finite Group DatabasebetaFinite Group Databasebeta| order | 5120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C25 |
| direct product | C2×#72220361 |
| Fitting, Sylow | C2×#6342371 ⋊ C5 |
| derived | C28 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72220361 |
| commutator, cosocle, hypocenter | C28 | C22×C5 |
| Frattini | C24 | C22×C24⋊C5 |
| Fitting | C2×#6342371 | C5 |
| socle | C25 | C2×C24⋊C5 |
| LCS | G ▷ C28 | |
| UCS | C1 ◁ C2 | |
At least 9484 conjugacy classes of subgroups; only the 17 normal subgroups are shown.
This group has at least 9484 conjugacy classes of subgroups — too many to draw. Only its 17 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
80 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72227520 |
| maximal normal subgroup of | C2×#72227520 |
Past the SmallGroups library coverage — no SmallGroups id.