Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9914 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#9929 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | #120 |
| commutator, Frattini, cosocle | C23×C4 | C23×C5 |
| prime radical | C24×C5 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ C23×C4×C5 ◁ G | |
610 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5)(6,7)(8,9)(10,11,15,18)(12,19,21,24)(13,17,14,22)(16,23,25,20)(26,27)(28,31)(29,32)(30,33)(34,37)(35,38)(36,40)(39,41);(10,12,15,21)(11,16,18,25)(13,20,14,23)(17,24,22,19)(26,28,30,35)(27,31,33,38)(29,34,36,41)(32,39,40,37);(7,9)(10,13,15,14)(11,17,18,22)(12,20,21,23)(16,24,25,19)(26,29)(27,32)(28,34)(30,36)(31,37)(33,40)(35,41)(38,39)200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 2917);