Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19883 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×#19897 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C5 |
| prime radical | C5×#550 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C42×C5 ◁ G | |
638 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 640 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2,3,4,5)(6,7,9,12)(8,10,13,11)(14,15,19,17)(16,22,23,29)(18,26,28,21)(20,27,25,24);(14,16,19,23)(15,20,17,25)(18,27,28,24)(21,29,26,22);(7,10)(8,13)(11,12)(16,23)(20,25)(22,29)(24,27);(14,17,19,15)(16,22,23,29)(18,21,28,26)(20,27,25,24)215 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 12885);