Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C29 |
| direct product | C5×#34633 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C5 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C5 |
| socle | C23×C5 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C5 ◁ G | |
3166 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)(10,11)(12,13)(14,15)(16,19)(17,21)(18,20)(22,25)(23,26)(24,27)(28,29);(6,7,8,9)(14,16)(15,19)(17,23)(18,22)(20,25)(21,26)(24,28)(27,29);(11,13)(16,22)(19,25)(23,28)(26,29);(15,20)(19,25)(21,27)(26,29);(14,17,18,24)(15,21,20,27)(16,23,22,28)(19,26,25,29)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 27621);