Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1468 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C5×#1473 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C2×C22⋊C4 |
| commutator | C23 | C23×C4×C5 |
| Frattini, cosocle | C22×C4 | C24×C5 |
| prime radical | C25×C5 | C2×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ C22×C42×C5 ◁ G | |
1066 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2)(35,36,37,38,39);(3,4,6,11,8,12,18,25)(5,10,15,23,13,24,26,34)(7,9,17,20,14,21,28,32)(16,19,30,31,27,22,29,33);(4,9)(5,13)(6,17)(10,22)(12,21)(15,29)(16,27)(18,28)(19,24)(23,34)(26,30)(31,33);(3,5,14,27)(4,10,21,22)(6,15,28,29)(7,16,8,13)(9,19,12,24)(11,23,32,33)(17,30,18,26)(20,31,25,34)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 10367);