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×#62839 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6616 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)(26,35)(27,28)(29,37)(30,31)(32,36)(33,39)(34,38);(11,18)(15,20)(16,22)(21,23)(25,31)(26,36)(28,33)(34,37);(8,9)(10,14)(11,15)(12,13)(16,21)(17,19)(18,20)(22,23)(24,26)(25,32)(27,37)(28,38)(29,33)(30,36)(31,35)(34,39);(8,10,12,17)(9,14,13,19)(11,16,18,22)(15,21,20,23)(24,27)(25,33)(26,37)(28,31)(29,32)(30,39)(34,36)(35,38);(8,11,12,18)(9,15,13,20)(10,16,17,22)(14,21,19,23)(24,28,30,33)(25,27,31,39)(26,38,36,29)(32,37,35,34);(8,9)(10,14)(11,15)(12,13)(16,21)(17,19)(18,20)(22,23)(24,29,30,38)(25,34,31,37)(26,33,36,28)(27,32,39,35)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55827);