Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10046 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#10061 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C5 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C5 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ C2×C42×C5 ◁ G | |
534 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1280 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5)(10,11,15,18)(12,19,21,24)(13,17,14,22)(16,23,25,20)(26,27,31,35)(28,36,39,40)(29,32,30,34)(33,37,41,38);(6,7)(8,9)(10,12,15,21)(11,16,18,25)(13,20,14,23)(17,24,22,19)(27,32)(29,30)(33,40)(34,35)(36,41)(37,38);(7,9)(10,13,15,14)(11,17,18,22)(12,20,21,23)(16,24,25,19)(26,28,31,39)(27,33,35,41)(29,38,30,37)(32,40,34,36)230 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 3049);