Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32712 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#32866 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C7×#376 ◁ G | |
562 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,11,14)(10,13,15,12)(16,17)(18,21)(19,20)(22,23)(24,25,28,27)(26,32,34,30)(29,31,37,36)(33,35,39,38);(8,10)(9,12)(11,15)(13,14)(17,20)(21,23)(24,26,28,34)(25,30,27,32)(29,38,37,35)(31,39,36,33);(8,10)(9,13)(11,15)(12,14)(17,20)(18,22)(24,27,28,25)(26,33,34,39)(29,31,37,36)(30,38,32,35);(10,15)(12,13)(16,18,19,22)(17,21,20,23)(25,27)(26,34)(31,36)(35,38)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 25854);