Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19755 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#19790 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×D42 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C42×C7 ◁ G | |
626 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,12,15)(10,16,19,22)(11,20,21,14)(13,17,23,18)(24,25,28,32)(26,29,34,38)(27,30,35,31)(33,36,39,37);(8,10,12,19)(9,13,15,23)(11,17,21,18)(14,22,20,16)(24,26,28,34)(25,29,32,38)(27,33,35,39)(30,36,31,37);(25,30)(27,35)(29,36)(31,32)(33,39)(37,38);(10,17)(11,21)(13,22)(14,20)(16,23)(18,19)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12778);