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×#62793 |
| 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 | |
7190 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)(16,20)(17,25)(18,22)(19,23)(21,26)(24,29)(27,28);(7,10)(11,13)(14,16,19,18)(15,20,23,22)(17,24,26,27)(21,28,25,29);(14,17,19,26)(15,21,23,25)(16,24,18,27)(20,28,22,29);(14,18,19,16)(15,22,23,20)(17,24,26,27)(21,28,25,29);(15,23)(20,22)(21,25)(28,29);(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, 55781);