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×#62888 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6906 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 6 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,13)(12,15)(16,17)(18,19)(20,26)(21,34)(22,23)(24,25)(27,35)(28,30)(29,38)(31,40)(32,36)(33,45)(37,39)(41,44)(42,46)(43,47);(8,9,11,13)(10,12,15,14)(17,23)(18,25)(20,32)(27,34)(29,40)(30,37)(33,44)(43,46);(8,9)(10,12)(11,13)(14,15)(16,18)(17,24)(19,23)(20,28)(21,29)(22,25)(26,37)(27,38)(30,36)(31,34)(32,39)(33,42)(35,40)(41,46)(43,45)(44,47);(8,10,11,15)(9,12,13,14)(16,19,22,24)(17,25,23,18)(20,30,32,37)(21,31,35,38)(26,39,36,28)(27,40,34,29)(33,43,44,46)(41,47,45,42);(16,20,22,32)(17,26,23,36)(18,28,25,39)(19,30,24,37)(21,33,35,44)(27,41,34,45)(29,42,40,47)(31,43,38,46);(16,21)(17,27)(18,29)(19,31)(20,33)(22,35)(23,34)(24,38)(25,40)(26,41)(28,42)(30,43)(32,44)(36,45)(37,46)(39,47)490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55876);