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×#62891 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6280 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)(8,9,13,14)(10,15,17,12)(11,19,21,16)(18,20,23,22)(24,25,30,35)(26,36,40,31)(27,28,33,32)(29,45,46,34)(37,38,41,43)(39,47,53,50)(42,48,49,44)(51,55,54,52);(9,14)(10,17)(16,19)(18,23)(24,26,30,40)(25,31,35,36)(27,37,33,41)(28,43,32,38)(29,39,46,53)(34,47,45,50)(42,51,49,54)(44,55,48,52);(8,10)(9,15)(11,18)(12,14)(13,17)(16,22)(19,20)(21,23)(24,26)(25,31)(27,41)(28,38)(29,39)(30,40)(32,43)(33,37)(34,47)(35,36)(42,54)(44,52)(45,50)(46,53)(48,55)(49,51);(8,11,13,21)(9,16,14,19)(10,18,17,23)(12,20,15,22)(24,27,30,33)(25,32,35,28)(26,37,40,41)(29,42,46,49)(31,38,36,43)(34,48,45,44)(39,51,53,54)(47,52,50,55);(24,28,30,32)(25,33,35,27)(26,38,40,43)(29,44,46,48)(31,37,36,41)(34,49,45,42)(39,52,53,55)(47,51,50,54);(8,12,13,15)(9,10,14,17)(11,20,21,22)(16,18,19,23)(24,29,30,46)(25,34,35,45)(26,39,40,53)(27,42,33,49)(28,44,32,48)(31,47,36,50)(37,51,41,54)(38,52,43,55)490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55879);