Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5×C8 · Schur multiplier (H2) = C24 |
| direct product | C5×#7932 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C5 | C22⋊C4 |
| commutator | C22 | C2×C4×C5×C8 |
| Frattini, cosocle | C2×C42 | C23×C5 |
| socle | C22×C5 | C2×#95 |
| prime radical | C24×C5 | C42 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C5 ◁ C22×C42×C5 ◁ G | |
666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,3,4,5)(6,7,9,12,11,13,10,8)(14,15)(16,24,26,20)(17,21)(18,23)(19,22)(25,29,27,28);(6,8,10,13,11,12,9,7)(14,16,18,27,19,26,17,25)(15,20,23,29,22,24,21,28);(14,17,19,18)(15,21,22,23)(16,25,26,27)(20,28,24,29)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 920);