Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62817 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C5 · Schur multiplier (H2) = C213 |
| direct product | C5×#62835 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ G | |
7148 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 6 generators on 29 points:
(1,2,3,4,5)(7,10)(11,13)(14,15,20,18)(16,23,21,17)(19,26,27,22)(24,25,28,29);(8,12)(11,13)(15,18)(16,21)(22,26)(24,28);(6,7)(8,11)(9,10)(12,13)(14,16)(15,17)(18,23)(19,24)(20,21)(22,25)(26,29)(27,28);(14,17,20,23)(15,21,18,16)(19,25,27,29)(22,28,26,24);(6,8,9,12)(7,11,10,13)(14,18,20,15)(16,23,21,17)(19,26,27,22)(24,29,28,25);(6,7)(8,11)(9,10)(12,13)(14,19)(15,22)(16,24)(17,25)(18,26)(20,27)(21,28)(23,29)380 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 55823);