Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C25 |
| direct product | C5×#11346 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C5 | C23 |
| commutator | C23 | C22×C5×C8 |
| Frattini, cosocle | C23×C4 | C23×C5 |
| socle, prime radical | C24×C5 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C5 ◁ G | |
878 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 1280 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,3,4,5)(6,7)(8,9)(14,15)(16,21)(17,19)(18,20)(22,23,24,26,25,27,28,29);(7,9)(10,11)(12,13)(14,16,18,17)(15,19,20,21);(7,9)(11,13)(14,17,18,16)(15,19,20,21)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 4334);