Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C5 · Schur multiplier (H2) = C213 |
| direct product | C2×C5×#3495 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C5 |
| prime radical | C2×C5×#525 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
7206 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 6 generators on 31 points:
(1,2)(27,28,29,30,31);(5,9)(7,10)(11,12,16,19)(13,14,21,17)(15,23,24,18)(20,25,26,22);(3,4,6,8)(5,7,9,10)(11,13,16,21)(12,17,19,14)(15,20,24,26)(18,25,23,22);(3,5)(4,7)(6,9)(8,10)(11,14)(12,13)(15,22)(16,17)(18,20)(19,21)(23,26)(24,25);(11,13)(12,14)(15,20)(16,21)(17,19)(18,22)(23,25)(24,26);(11,15,16,24)(12,18,19,23)(13,20,21,26)(14,22,17,25)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 55791);