Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C5 · Schur multiplier (H2) = C28 |
| direct product | C5×#60275 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C5 | C25 |
| commutator | C22 | C24×C4×C5 |
| Frattini, cosocle | C2×C4 | C25×C5 |
| socle | C22×C5 | C24×C4 |
| prime radical | C5×#3480 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C5 ◁ G | |
1818 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)(7,10)(8,12)(14,15,17,21,18,22,25,29)(16,19,24,26,23,20,27,28);(6,7)(8,11)(9,10)(12,13)(14,16)(15,19)(17,24)(18,23)(20,22)(21,26)(25,27)(28,29);(7,10)(11,13)(14,16)(15,20)(17,24)(18,23)(19,22)(21,28)(25,27)(26,29);(6,8,9,12)(7,11,10,13)(14,16)(15,19)(17,24)(18,23)(20,22)(21,26)(25,27)(28,29);(16,23)(19,20)(24,27)(26,28)380 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 53263);