Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62817 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C7×#62831 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6528 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)(9,13)(11,18)(14,19)(17,22)(24,25,30,35)(26,36,38,31)(27,34,29,32)(28,33,37,39);(10,16)(14,19)(17,22)(21,23)(24,25)(26,36)(27,32)(28,39)(29,34)(30,35)(31,38)(33,37);(8,9,12,13)(10,14,16,19)(11,15,18,20)(17,21,22,23)(24,26,30,38)(25,31,35,36)(27,37,29,28)(32,39,34,33);(24,27,30,29)(25,32,35,34)(26,37,38,28)(31,39,36,33);(8,10)(9,14)(11,17)(12,16)(13,19)(15,21)(18,22)(20,23)(24,28)(25,33)(26,27)(29,38)(30,37)(31,32)(34,36)(35,39);(8,11)(9,15)(10,17)(12,18)(13,20)(14,21)(16,22)(19,23)(24,29,30,27)(25,34,35,32)(26,28,38,37)(31,33,36,39)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55819);