Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#66243 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | (C24⋊C5)⋊C2 |
| commutator, hypocenter | 2−1+4⋊C5 | C2×C4 |
| Frattini, socle | C22 | C2×(C24⋊C5)⋊C2 |
| Fitting | C4×2−1+4 | D5 |
| prime radical, cosocle | C2×2−1+4⋊C5 | C22 |
| LCS | G ▷ 2−1+4⋊C5 | |
| UCS | C1 ◁ C2×C4 | |
408 conjugacy classes of subgroups; only the 19 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 19 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 256 |
56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116410);