Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1902 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C24×C4 |
| direct product | C5×#10955 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C5 | #386 |
| commutator | C2×C4 | C2×C42×C5 |
| Frattini, cosocle | C23×C4 | C23×C5 |
| socle | C2×C5 | #1437 |
| prime radical | C22×C5×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C5 ◁ C23×C4×C5 ◁ G | |
900 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5)(6,7,10,17,12,15,11,16)(8,13,20,28,19,29,25,27)(9,21,23,14,22,30,24,31)(18,32,33,26,34,35,36,37);(6,8,11,20,12,19,10,25)(7,13,17,27,15,29,16,28)(9,18,24,33,22,34,23,36)(14,26,30,32,31,37,21,35);(6,9,12,22)(7,14)(8,18,19,34)(10,23,11,24)(13,26)(15,31)(16,21)(17,30)(20,33,25,36)(27,32)(28,35)(29,37)290 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 3943);