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×#62889 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| prime radical | C7×#3455 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6186 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 6 generators on 55 points:
(1,2,3,4,5,6,7)(8,9,13,15)(10,16,18,11)(12,20,21,14)(17,19,23,22)(24,25,29,30)(26,34,37,31)(27,32,38,42)(28,40,41,33)(35,46,48,43)(36,44,50,47)(39,52,51,45)(49,53,55,54);(8,10,13,18)(9,11,15,16)(12,17,21,23)(14,19,20,22)(25,30)(27,38)(31,34)(33,40)(35,48)(39,51)(44,47)(49,55);(8,11)(9,10)(12,19)(13,16)(14,17)(15,18)(20,23)(21,22)(24,25)(26,34)(27,32)(28,33)(29,30)(31,37)(35,46)(36,47)(38,42)(39,45)(40,41)(43,48)(44,50)(49,54)(51,52)(53,55);(8,12,13,21)(9,14,15,20)(10,17,18,23)(11,19,16,22)(24,26,29,37)(25,31,30,34)(27,35,38,48)(28,36,41,50)(32,43,42,46)(33,44,40,47)(39,49,51,55)(45,53,52,54);(24,27,29,38)(25,32,30,42)(26,35,37,48)(28,39,41,51)(31,43,34,46)(33,45,40,52)(36,49,50,55)(44,53,47,54);(24,28)(25,33)(26,36)(27,39)(29,41)(30,40)(31,44)(32,45)(34,47)(35,49)(37,50)(38,51)(42,52)(43,53)(46,54)(48,55)490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55877);