Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #36702 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#36819 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
1680 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7)(10,14)(13,15)(17,21)(19,23)(24,25,29,32)(26,30,34,28)(27,35,37,31)(33,36,39,38);(9,12)(13,15)(17,21)(18,22)(24,26,29,34)(25,28,32,30)(27,33,37,39)(31,36,35,38);(8,9)(10,13)(11,12)(14,15)(16,17,20,21)(18,19,22,23)(24,26)(25,30)(27,33)(28,32)(29,34)(31,38)(35,36)(37,39);(8,9)(10,13)(11,12)(14,15)(16,18,20,22)(17,19,21,23)(24,27,29,37)(25,31,32,35)(26,33,34,39)(28,36,30,38);(8,10)(9,13)(11,14)(12,15)(16,19)(17,22)(18,21)(20,23)(24,28,29,30)(25,26,32,34)(27,36,37,38)(31,33,35,39)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29807);