Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #34980 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C26×C4 |
| direct product | C5×#35296 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C5 |
| prime radical | C5×#2619 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
1894 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 640 |
A minimal faithful permutation representation — 5 generators on 29 points:
(1,2,3,4,5)(8,12)(11,13)(15,19)(17,20)(23,24)(27,28);(7,10)(11,13)(15,19)(16,21)(22,23,26,24)(25,27,29,28);(6,7)(8,11)(9,10)(12,13)(14,15)(16,20)(17,21)(18,19)(22,24,26,23)(25,28,29,27);(6,7)(8,11)(9,10)(12,13)(14,16,18,21)(15,20,19,17)(22,25,26,29)(23,27,24,28);(6,8,9,12)(7,11,10,13)(14,17,18,20)(15,21,19,16)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 28284);