Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60460 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C28 |
| direct product | C5×#60668 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C5 |
| prime radical | C2×C5×#41 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C4×C5×#41 ◁ G | |
1790 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)(6,7,9,11)(8,12,13,10)(15,19)(17,24)(20,25)(21,26)(23,28)(27,29);(6,8,9,13)(7,10,11,12)(15,20)(19,25)(21,27)(26,29);(14,15,17,19,18,20,24,25)(16,21,23,26,22,27,28,29);(14,16)(15,21)(17,23)(18,22)(19,26)(20,27)(24,28)(25,29);(16,22)(21,27)(23,28)(26,29)290 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 53656);