Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C5 · Schur multiplier (H2) = C213 |
| direct product | C5×#62850 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ G | |
6846 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 6 generators on 45 points:
(1,2,3,4,5)(7,10)(11,13)(15,20)(18,30)(21,24)(22,31)(26,40)(29,41)(33,36)(39,45);(6,7)(8,11)(9,10)(12,13)(17,28)(22,31)(25,38)(29,41)(33,36)(35,42)(39,45)(43,44);(14,15,19,20)(16,24,27,21)(17,22,28,31)(18,23,30,32)(25,36,38,33)(26,37,40,34)(29,35,41,42)(39,44,45,43);(14,16,19,27)(15,21,20,24)(17,25,28,38)(18,26,30,40)(22,33,31,36)(23,34,32,37)(29,39,41,45)(35,43,42,44);(6,8,9,12)(7,11,10,13)(14,17)(15,22)(16,25)(18,29)(19,28)(20,31)(21,33)(23,35)(24,36)(26,39)(27,38)(30,41)(32,42)(34,43)(37,44)(40,45);(14,18)(15,23)(16,26)(17,29)(19,30)(20,32)(21,34)(22,35)(24,37)(25,39)(27,40)(28,41)(31,42)(33,43)(36,44)(38,45)410 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 55838);