Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23876 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#24087 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C5 |
| prime radical | C5×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G | |
984 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2,3,4,5)(6,7)(8,13)(9,11)(10,12)(14,15)(16,17)(18,22)(19,23)(20,24)(21,27)(25,29)(26,28);(6,8,10,9)(7,11,12,13)(14,16,20,26)(15,17,24,28)(18,21,19,25)(22,27,23,29);(6,9,10,8)(7,11,12,13)(14,17)(15,21)(16,23)(18,27)(19,29)(20,28)(22,26)(24,25);(7,12)(11,13)(14,18,20,19)(15,22,24,23)(16,21,26,25)(17,27,28,29)215 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 17075);