Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #14715 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×#14781 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C5 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C5 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C5 ◁ G | |
1274 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)(7,9)(14,15,18,19)(16,17,21,20)(22,23,26,28)(24,27,29,25);(11,13)(15,19)(16,21)(22,24,26,29)(23,25,28,27);(10,11)(12,13)(14,16,18,21)(15,20,19,17)(22,24)(23,27)(25,28)(26,29);(6,7)(8,9)(14,17,18,20)(15,21,19,16)(22,25,26,27)(23,24,28,29)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 7769);