Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×#10617013 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C23 | (C24⋊C5)⋊C2 |
| commutator, cosocle, hypocenter | #564⋊C5 | C22 |
| Frattini | C22 | C2×(C24⋊C5)⋊C2 |
| Fitting | C2×#564 | D5 |
| prime radical | C2×#564⋊C5 | C2 |
| LCS | G ▷ #564⋊C5 | |
| UCS | C1 ◁ C23 | |
275 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 275 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 256 |
44 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116389);