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×#62833 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ G | |
7050 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)(15,20)(16,24)(17,27)(23,28);(8,12)(11,13)(14,15,19,20)(16,25,24,21)(17,22,27,29)(18,28,26,23);(6,7)(8,11)(9,10)(12,13)(14,16,19,24)(15,21,20,25)(17,26,27,18)(22,28,29,23);(14,17)(15,22)(16,26)(18,24)(19,27)(20,29)(21,28)(23,25);(6,8,9,12)(7,11,10,13)(14,18,19,26)(15,23,20,28)(16,17,24,27)(21,22,25,29);(6,7)(8,11)(9,10)(12,13)(14,17)(15,22)(16,26)(18,24)(19,27)(20,29)(21,28)(23,25)380 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 55821);