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×#18455 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C5 |
| prime radical | C5×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G | |
894 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)(6,7)(8,11)(9,12)(10,13)(14,20)(15,18)(16,19)(17,21)(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);(6,8)(7,11)(9,14)(10,15)(12,17)(13,18)(16,21)(19,20)(22,24)(23,29)(25,35)(26,36)(27,41)(28,37)(30,42)(31,34)(32,47)(33,43)(38,49)(39,51)(40,50)(44,52)(45,53)(46,48);(6,9)(7,12)(8,14)(10,16)(11,17)(13,19)(15,21)(18,20)(22,25,28,39)(23,30,33,45)(24,35,37,51)(26,40,27,38)(29,42,43,53)(31,46,32,44)(34,48,47,52)(36,50,41,49);(7,13)(11,18)(12,19)(17,20)(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, 11443);