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×#35310 |
| 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 | |
2346 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)(10,11,15,14)(12,17,16,13)(18,19)(20,23)(21,24)(22,27)(25,30)(26,28)(29,32)(31,33);(10,12)(11,13)(14,17)(15,16)(19,20)(21,28)(25,27)(29,33);(6,7)(8,9)(10,13,15,17)(11,16,14,12)(18,20,23,19)(21,26,28,24)(22,27,30,25)(29,32,33,31);(10,14,15,11)(12,17,16,13)(18,21,23,28)(19,24,20,26)(22,29,30,33)(25,31,27,32);(18,22,23,30)(19,25,20,27)(21,29,28,33)(24,31,26,32)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 28298);