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×#19801 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#550 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C42×C7 ◁ G | |
590 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(9,14)(10,12)(15,22)(16,20)(17,21)(18,23)(24,25,28,32)(26,29,34,38)(27,30,35,31)(33,36,39,37);(8,9,13,16)(10,14,12,20)(11,18,19,22)(15,21,23,17)(24,26,28,34)(25,29,32,38)(27,33,35,39)(30,36,31,37);(8,10,13,12)(9,14,16,20)(11,17,19,21)(15,22,23,18)(25,30)(27,35)(29,36)(31,32)(33,39)(37,38);(8,11,13,19)(9,15,16,23)(10,17,12,21)(14,22,20,18)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12789);