Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | D5×#1655 |
| Fitting | C5×#1655 ⋊ C2 |
| Sylow | C5 ⋊ C2×#1655 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D5×#120 |
| commutator, cosocle | C42×C5 | C24 |
| Frattini | C42 | C23×D5 |
| Fitting | C5×#1655 | C2 |
| socle | C22×C5 | C2×#120 |
| hypercenter | #1655 | D5 |
| hypocenter | C5 | C2×#1655 |
| LCS | G ▷ C42×C5 ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #1655 | |
1330 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 1330 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 150681);