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×#62841 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6624 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)(14,19)(15,20)(21,23)(24,25,29,30)(26,33,28,31)(27,32,35,37)(34,39,36,38);(11,18)(15,20)(16,22)(21,23)(25,30)(27,35)(31,33)(34,36);(8,9)(10,14)(11,15)(12,13)(16,21)(17,19)(18,20)(22,23)(24,25)(26,31)(27,32)(28,33)(29,30)(34,38)(35,37)(36,39);(8,10,12,17)(9,14,13,19)(11,16,18,22)(15,21,20,23)(24,26,29,28)(25,31,30,33)(27,34,35,36)(32,38,37,39);(8,11,12,18)(9,15,13,20)(10,16,17,22)(14,21,19,23)(24,27)(25,32)(26,34)(28,36)(29,35)(30,37)(31,38)(33,39);(8,9)(10,14)(11,15)(12,13)(16,21)(17,19)(18,20)(22,23)(24,28,29,26)(25,33,30,31)(27,36,35,34)(32,39,37,38)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55829);