Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1812 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C26 |
| direct product | C2×C5×#1813 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C5 | #117 |
| commutator | C2×C4 | C23×C4×C5 |
| Frattini, cosocle | C22×C4 | C24×C5 |
| socle | C22×C5 | #380 |
| prime radical | C22×C5×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C5 ◁ C22×C5×M16 ◁ G | |
1314 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2)(35,36,37,38,39);(3,4,8,12,9,13,7,22)(5,14,17,25,18,29,16,10)(6,19,20,26,21,11,23,27)(15,30,31,34,32,28,33,24);(3,5,7,16,9,18,8,17)(4,10,12,14,13,25,22,29)(6,15,20,31,21,32,23,33)(11,24,26,28,19,34,27,30);(3,6)(4,11)(5,15)(7,20)(8,23)(9,21)(10,24)(12,26)(13,19)(14,28)(16,31)(17,33)(18,32)(22,27)(25,34)(29,30)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 13660);