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×#62830 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ G | |
7264 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)(6,7)(8,10)(9,13)(11,12)(15,19)(17,24)(20,25)(23,28);(7,12)(8,13)(16,22)(20,25)(23,28)(27,29);(6,8,11,13)(7,9,12,10)(14,15,18,19)(16,20,22,25)(17,21,24,26)(23,27,28,29);(6,9,11,10)(7,8,12,13);(6,7)(8,9)(10,13)(11,12)(14,16)(15,20)(17,23)(18,22)(19,25)(21,27)(24,28)(26,29);(6,10,11,9)(7,13,12,8)(14,17)(15,21)(16,23)(18,24)(19,26)(20,27)(22,28)(25,29)380 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 55818);