Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #36702 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#36782 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C22×C7×D4 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
1518 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7)(10,14)(13,15)(17,20)(21,23)(24,25,29,32)(26,33,27,30)(28,36,37,31)(34,38,35,39);(9,12)(13,15)(24,26,29,27)(25,30,32,33)(28,34,37,35)(31,38,36,39);(8,9)(10,13)(11,12)(14,15)(16,17)(18,21)(19,20)(22,23)(24,27,29,26)(25,30,32,33)(28,35,37,34)(31,38,36,39);(8,9)(10,13)(11,12)(14,15)(16,18,19,22)(17,21,20,23)(24,25)(26,33)(27,30)(28,31)(29,32)(34,39)(35,38)(36,37);(8,10)(9,13)(11,14)(12,15)(24,28)(25,31)(26,34)(27,35)(29,37)(30,38)(32,36)(33,39)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29770);