Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C5 · Schur multiplier (H2) = C28 |
| direct product | C5×#34491 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C5 | C25 |
| commutator | C22 | C24×C4×C5 |
| Frattini, cosocle | C23 | C25×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
1956 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1280 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2,3,4,5)(6,7,9,8)(11,14)(12,13)(19,23)(21,29)(24,26)(27,33);(10,11,15,14)(12,17,13,16)(18,19)(20,26)(21,25)(22,23)(24,28)(27,32)(29,30)(31,33);(10,12,15,13)(11,16,14,17);(6,8,9,7)(10,13,15,12)(11,17,14,16)(18,20,22,28)(19,24,23,26)(21,27,29,33)(25,31,30,32);(10,14,15,11)(12,17,13,16)(18,21,22,29)(19,25,23,30)(20,27,28,33)(24,31,26,32)380 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 27479);