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×#36798 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C22×C7×D4 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
1518 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)(26,33,36,31)(27,37,32,28)(34,35,38,39);(9,12)(13,15)(16,17,20,19)(18,21,22,23)(25,30)(27,32)(31,33)(34,38);(8,9)(10,13)(11,12)(14,15)(16,18)(17,21)(19,23)(20,22)(24,26,29,36)(25,31,30,33)(27,34,32,38)(28,35,37,39);(8,9)(10,13)(11,12)(14,15)(16,19,20,17)(18,23,22,21)(24,27,29,32)(25,28,30,37)(26,34,36,38)(31,35,33,39);(8,10)(9,13)(11,14)(12,15)(24,28)(25,32)(26,35)(27,30)(29,37)(31,38)(33,34)(36,39)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29786);