Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #34980 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C29 |
| direct product | C5×#35308 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C5 |
| prime radical | C2×C5×#537 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
2974 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 640 |
A minimal faithful permutation representation — 5 generators on 29 points:
(1,2,3,4,5)(7,9)(11,12)(14,15,19,21)(16,22,23,17)(18,26,27,20)(24,25,29,28);(10,11,13,12)(16,23)(17,22)(24,29)(25,28);(6,7)(8,9)(10,12,13,11)(14,16)(15,17)(18,24)(19,23)(20,25)(21,22)(26,28)(27,29);(14,17)(15,16)(18,25)(19,22)(20,24)(21,23)(26,29)(27,28);(14,18,19,27)(15,20,21,26)(16,24,23,29)(17,25,22,28)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 28296);