Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9946 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#9961 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C5 |
| prime radical | C24×C5 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G | |
552 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5)(6,7)(8,11)(9,12)(10,13)(14,17)(15,18)(16,20)(19,21)(22,23,27,31)(24,32,35,36)(25,28,26,30)(29,33,37,34);(6,8,10,15)(7,11,13,18)(9,14,16,21)(12,19,20,17)(23,28)(25,26)(29,36)(30,31)(32,37)(33,34);(6,9)(7,12)(8,14)(10,16)(11,17)(13,20)(15,21)(18,19)(22,24,27,35)(23,29,31,37)(25,34,26,33)(28,36,30,32)185 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 2949);