Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#18473 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C5 |
| prime radical | C5×#538 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G | |
846 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5)(7,11)(9,16)(12,20)(13,17)(15,18)(19,21)(22,23,28,33)(24,34,37,47)(25,30,39,45)(26,32,27,31)(29,41,43,36)(35,48,51,52)(38,46,40,44)(42,49,53,50);(6,7,10,13)(8,12,14,21)(9,17,16,11)(15,19,18,20)(22,24,28,37)(23,29,33,43)(25,35,39,51)(26,36,27,41)(30,42,45,53)(31,34,32,47)(38,49,40,50)(44,52,46,48);(6,8)(7,12)(9,18)(10,14)(11,19)(13,21)(15,16)(17,20)(22,25)(23,30)(24,35)(26,40)(27,38)(28,39)(29,42)(31,46)(32,44)(33,45)(34,48)(36,50)(37,51)(41,49)(43,53)(47,52);(8,14)(12,21)(15,18)(19,20)(22,26,28,27)(23,31,33,32)(24,36,37,41)(25,38,39,40)(29,34,43,47)(30,44,45,46)(35,49,51,50)(42,52,53,48)170 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 11461);