Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2002 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C27 |
| direct product | C2×C5×#2002 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C5 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ C23×C4×C5 ◁ G | |
2750 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2)(15,16,17,18,19);(3,4)(5,6)(7,8)(9,11)(10,13)(12,14);(8,11)(9,14)(12,13);(4,6)(9,14)(11,12)260 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C5×#23872 |
| maximal normal subgroup of | C2×C5×#23872 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 16383);