Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #34980 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C28 |
| direct product | C5×#35311 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C5 |
| prime radical | C25×C5 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
2462 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2,3,4,5)(7,9)(12,16)(14,17)(18,19,22,25)(20,23,28,26)(21,29,30,24)(27,32,33,31);(6,7)(8,9)(10,11,13,15)(12,14,16,17)(18,19,22,25)(20,26,28,23)(21,24,30,29)(27,32,33,31);(10,12)(11,14)(13,16)(15,17)(18,19)(20,23)(21,24)(22,25)(26,28)(27,31)(29,30)(32,33);(18,20)(19,23)(21,27)(22,28)(24,31)(25,26)(29,32)(30,33);(18,21,22,30)(19,24,25,29)(20,27,28,33)(23,31,26,32)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 28299);