Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62862 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C7×#62870 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6730 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 6 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,18)(12,13)(15,19)(16,20)(17,23)(21,22)(24,25,28,29)(26,30,34,32)(27,35,36,31)(33,38,39,37);(10,16)(14,20)(17,22)(21,23)(24,25)(26,32)(27,31)(28,29)(30,34)(33,38)(35,36)(37,39);(9,13)(14,20)(15,18)(21,23)(25,29)(30,32)(31,35)(37,38);(8,9)(10,14)(11,15)(12,13)(16,20)(17,21)(18,19)(22,23)(24,25)(26,30)(27,31)(28,29)(32,34)(33,37)(35,36)(38,39);(8,10)(9,14)(11,17)(12,16)(13,20)(15,21)(18,23)(19,22)(24,26,28,34)(25,30,29,32)(27,33,36,39)(31,37,35,38);(8,11)(9,15)(10,17)(12,19)(13,18)(14,21)(16,22)(20,23)(24,27,28,36)(25,31,29,35)(26,33,34,39)(30,37,32,38)490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55858);