Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62817 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C5 · Schur multiplier (H2) = C213 |
| direct product | C5×#62836 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ G | |
7254 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 6 generators on 29 points:
(1,2,3,4,5)(7,10)(11,13)(14,15)(16,25)(17,18)(19,27)(20,21)(22,26)(23,29)(24,28);(8,12)(11,13)(15,21)(16,26)(18,23)(24,27);(6,7)(8,11)(9,10)(12,13)(14,16)(15,22)(17,27)(18,28)(19,23)(20,26)(21,25)(24,29);(14,17)(15,23)(16,27)(18,21)(19,22)(20,29)(24,26)(25,28);(6,8,9,12)(7,11,10,13)(14,18,20,23)(15,17,21,29)(16,28,26,19)(22,27,25,24);(6,7)(8,11)(9,10)(12,13)(14,19,20,28)(15,24,21,27)(16,23,26,18)(17,22,29,25)380 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 55824);