Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#10458 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C5 |
| prime radical | C5×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G | |
428 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 640 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,3,4,5)(6,7)(8,10)(9,12)(11,13)(14,15)(16,17)(18,27)(19,22)(20,23)(21,29)(24,26)(25,28);(14,16,19,24)(15,20,22,25)(17,21,26,27)(18,28,29,23);(7,10)(8,13)(11,12)(14,17,18,25,19,26,29,20)(15,16,21,23,22,24,27,28)200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 3446);