Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C22×C42 |
| direct product | C5×#14356 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C5 | C24 |
| commutator | C23 | C23×C4×C5 |
| Frattini, cosocle | C24 | C24×C5 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C5 ◁ G | |
1262 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 1280 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2,3,4,5)(15,18)(19,21)(22,23,25,27)(24,26,29,28);(10,11,12,13)(22,23)(24,26)(25,27)(28,29);(6,7,8,9)(10,11)(12,13)(14,15,17,18)(16,19,20,21)(22,23)(24,28)(25,27)(26,29);(14,16,17,20)(15,19,18,21)(22,24,25,29)(23,26,27,28)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 7344);