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×#62877 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6394 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)(25,29)(27,35)(30,32)(33,39);(10,16)(14,20)(17,22)(21,23)(24,25,28,29)(26,32,34,30)(27,31,35,36)(33,38,39,37);(9,13)(14,20)(15,18)(21,23)(24,26,28,34)(25,30,29,32)(27,33,35,39)(31,37,36,38);(8,9)(10,14)(11,15)(12,13)(16,20)(17,21)(18,19)(22,23)(24,27)(25,31)(26,33)(28,35)(29,36)(30,37)(32,38)(34,39);(8,10,12,16)(9,14,13,20)(11,17,19,22)(15,21,18,23);(8,11)(9,15)(10,17)(12,19)(13,18)(14,21)(16,22)(20,23)490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55865);