Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25 |
| direct product | C2×C5×#1554 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C2×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C5 |
| Frattini, cosocle | C42 | C24×C5 |
| prime radical | C24×C5 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ C22×C42×C5 ◁ G | |
974 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 640 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2)(35,36,37,38,39);(3,4,7,10,8,11,6,15)(5,12,13,17,14,9,16,18)(19,20)(21,27)(22,30)(23,25)(24,28)(26,32)(29,34)(31,33);(3,5,8,14)(4,9,11,12)(6,13,7,16)(10,17,15,18)(19,21,23,29)(20,24,25,33)(22,31,32,28)(26,34,30,27);(3,6,8,7)(4,10,11,15)(5,13,14,16)(9,17,12,18)(20,25)(24,33)(26,30)(27,34)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 10700);