Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C5 · Schur multiplier (H2) = C213 |
| direct product | C2×C5×#3566 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
6694 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 6 generators on 39 points:
(1,2)(35,36,37,38,39);(4,10)(5,15)(6,20)(7,23)(11,28)(12,18)(14,27)(16,26)(19,32)(21,29)(22,33)(24,34);(3,4)(5,16)(6,21)(7,13)(8,10)(9,14)(11,15)(12,22)(17,23)(18,20)(19,28)(24,30)(25,27)(26,32)(29,33)(31,34);(3,5,8,19)(4,11,10,26)(6,17,22,13)(7,18,23,29)(9,15,25,32)(12,24,21,34)(14,16,27,28)(20,31,33,30);(3,6)(4,12)(5,17)(7,16)(8,22)(9,20)(10,21)(11,24)(13,19)(14,29)(15,31)(18,27)(23,28)(25,33)(26,34)(30,32);(3,7,9,24)(4,13,14,30)(5,18,15,21)(6,16,20,11)(8,23,25,34)(10,17,27,31)(12,19,29,32)(22,28,33,26)380 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 55730);