Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C5 · Schur multiplier (H2) = C213 |
| direct product | C5×#62851 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ G | |
7066 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)(16,19)(17,18)(20,28)(21,23)(22,29)(24,25)(26,27);(6,7,9,10)(8,11,12,13)(14,16,21,18)(15,17,23,19)(20,24,29,26)(22,25,28,27);(14,17,21,19)(15,16,23,18)(20,25,29,27)(22,24,28,26);(14,18,21,16)(15,17,23,19)(20,26,29,24)(22,25,28,27);(6,8,9,12)(7,11,10,13)(14,19,21,17)(15,16,23,18)(20,27,29,25)(22,24,28,26);(14,20)(15,22)(16,24)(17,25)(18,26)(19,27)(21,29)(23,28)410 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 55839);