Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5×C8 · Schur multiplier (H2) = C24 |
| direct product | C5×C8×#125 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C5×C8 | C23 |
| commutator | C22 | C23×C5×C8 |
| Frattini, cosocle | C22×C4 | C24×C5 |
| socle, prime radical | C23×C5 | C23×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5×C8 ◁ G | |
742 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 1280 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2,3,4,5)(6,7,8,9,10,11,12,13);(16,20)(18,21)(22,23,25,27)(24,26,28,29);(14,15,17,19)(16,18,20,21)(22,23)(24,26)(25,27)(28,29);(14,16)(15,18)(17,20)(19,21)(22,24,25,28)(23,26,27,29)560 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 14660);