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×#62822 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ G | |
7274 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)(8,12)(9,10)(11,13)(14,15)(16,17)(18,26)(19,20)(21,22)(23,27)(24,28)(25,29);(7,10)(11,12)(15,20)(16,22)(23,26)(24,29);(6,7)(8,11)(9,10)(12,13)(14,16,19,22)(15,21,20,17)(18,24,27,29)(23,28,26,25);(6,8,9,13)(7,11,10,12)(14,17,19,21)(15,22,20,16)(18,25,27,28)(23,29,26,24);(14,15)(16,21)(17,22)(18,23)(19,20)(24,28)(25,29)(26,27);(14,18)(15,23)(16,24)(17,25)(19,27)(20,26)(21,28)(22,29)380 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 55810);