Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C8 |
| direct product | D5×#1455 |
| Fitting | C5×#1455 ⋊ C2 |
| Sylow | C5 ⋊ C2×#1455 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C23×D5 |
| commutator, socle | C22×C5 | C22×C42 |
| Fitting | C5×#1455 | C2 |
| prime radical | C23×D5 | C42 |
| cosocle | C42×C5 | C24 |
| hypercenter | #1455 | D5 |
| hypocenter | C5 | C2×#1455 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C42 ◁ #1455 | |
994 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C5⋊D5×#1455, D5×#19745, #72221445, … |
| maximal normal subgroup of | D5×#19745, #72221445, AGL(1,𝔽5)×#1455, … |
| maximal quotient of | C5⋊D5×#1455 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 135272);