Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C27 |
| direct product | C5×#23889 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C5 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C22×C4×C5 ◁ G | |
1648 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5)(6,7)(8,9)(10,11)(12,22)(13,27)(14,21)(15,20)(16,25)(17,29)(18,28)(19,32)(23,38)(24,33)(26,35)(30,37)(31,34)(36,40)(39,41);(10,12,15,26)(11,16,20,34)(13,24,29,39)(14,31,32,25)(17,36,27,38)(18,33,37,41)(19,35,21,22)(23,28,40,30);(7,9)(10,13)(11,17)(12,23)(14,28)(15,29)(16,33)(18,19)(20,27)(21,37)(22,36)(24,31)(25,39)(26,40)(30,32)(34,41)(35,38);(10,13)(11,18)(12,24)(14,30)(15,29)(16,33)(17,19)(20,37)(21,27)(22,38)(23,31)(25,40)(26,39)(28,32)(34,41)(35,36)215 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 16877);