Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23882 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C27 |
| direct product | C5×#23885 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C5 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5 ◁ C22×C4×C5 ◁ G | |
1662 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5)(6,7)(8,19)(9,24)(10,27)(11,17)(12,16)(13,18)(14,22)(15,26)(20,29)(21,30)(23,33)(25,32)(28,31)(34,36)(35,37);(6,8)(7,14)(9,20)(10,21)(11,28)(12,22)(13,23)(15,30)(16,33)(17,19)(18,31)(24,34)(25,37)(26,36)(27,35)(29,32);(6,9,13,10)(7,15,18,32)(8,20,23,21)(11,26,12,25)(14,29,31,30)(16,24,17,27)(19,34,33,35)(22,37,28,36);(6,10,13,9)(7,15,18,32)(8,21,23,20)(11,25,12,26)(14,30,31,29)(16,24,17,27)(19,35,33,34)(22,36,28,37)200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 16873);