Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C5 · Schur multiplier (H2) = C214 |
| direct product | C5×#62848 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ G | |
10962 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 6 generators on 41 points:
(1,2,3,4,5)(7,9)(11,16)(14,26)(17,20)(18,27)(22,36)(25,37)(29,32)(35,41);(6,7)(8,9)(13,24)(18,27)(21,34)(25,37)(29,32)(31,38)(35,41)(39,40);(10,11,15,16)(12,20,23,17)(13,18,24,27)(14,19,26,28)(21,32,34,29)(22,33,36,30)(25,31,37,38)(35,40,41,39);(10,12,15,23)(11,17,16,20)(13,21,24,34)(14,22,26,36)(18,29,27,32)(19,30,28,33)(25,35,37,41)(31,39,38,40);(10,13)(11,18)(12,21)(14,25)(15,24)(16,27)(17,29)(19,31)(20,32)(22,35)(23,34)(26,37)(28,38)(30,39)(33,40)(36,41);(10,14)(11,19)(12,22)(13,25)(15,26)(16,28)(17,30)(18,31)(20,33)(21,35)(23,36)(24,37)(27,38)(29,39)(32,40)(34,41)410 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 55836);