Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C5 · Schur multiplier (H2) = C215 |
| direct product | C23×C5×#121 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25×C5 | C23 |
| commutator, Frattini, cosocle | C22 | C26×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C25×C5 ◁ G | |
19998 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 640 |
A minimal faithful permutation representation — 6 generators on 19 points:
(1,2)(15,16,17,18,19);(3,4);(5,6);(8,10)(12,14);(11,12,13,14);(7,8)(9,10)560 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 55644);