Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #34980 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C28×C4 |
| direct product | C5×#35329 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C5 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
3662 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 5 generators on 29 points:
(1,2,3,4,5)(7,9)(11,12)(17,24)(21,26)(23,28)(27,29);(10,11,13,12)(15,19)(16,22)(21,26)(23,28);(6,7,8,9)(10,12,13,11)(14,15,18,19)(16,20,22,25)(17,21,24,26)(23,27,28,29);(14,16)(15,20)(17,23)(18,22)(19,25)(21,27)(24,28)(26,29);(14,17,18,24)(15,21,19,26)(16,23,22,28)(20,27,25,29)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 28317);