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×#19814 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C2×C7×D8 | D4 |
| 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)(9,13)(11,19)(14,20)(15,16)(17,23)(21,22)(24,25,28,31)(26,32,34,39)(27,35,37,30)(29,36,38,33);(8,9)(10,14)(11,15)(12,16)(13,19)(17,21)(18,22)(20,23);(8,10,12,18)(9,14,16,22)(11,17,19,23)(13,20,15,21)(24,26,28,34)(25,29,31,38)(27,36,37,33)(30,39,35,32);(9,15)(11,19)(13,16)(14,21)(17,23)(20,22)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12802);