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×#36804 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C7×#392 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
1534 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)(18,22)(21,23)(24,25,29,30)(26,31,33,28)(27,35,37,32)(34,36,39,38);(9,12)(13,15)(16,17,20,19)(18,21,22,23)(25,30)(26,33)(32,35)(34,39);(8,9)(10,13)(11,12)(14,15)(16,18)(17,21)(19,23)(20,22)(24,26)(25,31)(27,34)(28,30)(29,33)(32,38)(35,36)(37,39);(8,9)(10,13)(11,12)(14,15)(16,19,20,17)(18,23,22,21)(24,27,29,37)(25,32,30,35)(26,34,33,39)(28,36,31,38);(8,10)(9,13)(11,14)(12,15)(24,28,29,31)(25,26,30,33)(27,36,37,38)(32,34,35,39)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29792);