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×#62821 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ G | |
7338 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)(16,25)(17,28)(18,19)(20,21)(22,26)(23,27)(24,29);(8,12)(11,13)(15,21)(16,26)(18,24)(23,28);(6,7)(8,11)(9,10)(12,13)(14,16)(15,22)(17,24)(18,27)(19,28)(20,26)(21,25)(23,29);(14,17,20,27)(15,23,21,28)(16,24,26,18)(19,22,29,25);(6,8)(7,11)(9,12)(10,13)(14,18,20,24)(15,19,21,29)(16,27,26,17)(22,28,25,23);(6,7)(8,11)(9,10)(12,13)(14,19)(15,24)(16,28)(17,22)(18,21)(20,29)(23,26)(25,27)380 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 55809);