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×#62819 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ G | |
7242 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 6 generators on 29 points:
(1,2,3,4,5)(7,10)(11,13)(14,15)(16,22)(17,19)(18,25)(20,24)(21,26)(23,27)(28,29);(8,12)(11,13)(14,16,19,24)(15,20,17,22)(18,23,26,29)(21,27,25,28);(6,7)(8,11)(9,10)(12,13)(14,17,19,15)(16,20,24,22)(18,25,26,21)(23,27,29,28);(14,18)(15,21)(16,23)(17,25)(19,26)(20,27)(22,28)(24,29);(6,8)(7,11)(9,12)(10,13)(14,16)(15,22)(17,20)(18,23)(19,24)(21,28)(25,27)(26,29);(6,7)(8,11)(9,10)(12,13)(14,18)(15,21)(16,23)(17,25)(19,26)(20,27)(22,28)(24,29)380 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 55807);