Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #36702 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C27 |
| direct product | C5×#36778 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C5 |
| prime radical | C2×C5×#120 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
1906 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)(6,7,9,11)(8,12,13,10)(16,20)(19,21)(23,26)(27,29);(6,8,9,13)(7,10,11,12)(15,18)(19,21);(14,15)(16,19)(17,18)(20,21)(22,23)(24,27)(25,26)(28,29);(6,8)(7,10)(9,13)(11,12)(14,15)(16,19)(17,18)(20,21)(22,24,25,28)(23,27,26,29);(6,7)(8,10)(9,11)(12,13)(14,16)(15,19)(17,20)(18,21)260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 29766);