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 | C5×#62805 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C5 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C5 |
| socle | C22×C5 | C26 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C5 ◁ G | |
7104 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)(6,7)(8,11)(9,10)(12,13)(14,15,18,21)(16,22,23,19)(17,25,26,20)(24,27,29,28);(7,10)(11,13);(14,16)(15,19)(17,24)(18,23)(20,27)(21,22)(25,28)(26,29);(16,23)(19,22)(24,29)(27,28);(14,17,18,26)(15,20,21,25)(16,24,23,29)(19,27,22,28);(6,8,9,12)(7,11,10,13)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 55793);