Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#10171 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C23×C7 | #121 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
488 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,12,15)(10,16,17,23)(11,19,20,14)(13,21,22,18)(25,30)(27,28)(31,34)(32,33)(35,36)(38,39);(11,20)(14,19)(16,23)(18,21)(24,25,29,33)(26,34,37,38)(27,32,28,30)(31,35,39,36);(8,10)(9,13)(11,21)(12,17)(14,23)(15,22)(16,19)(18,20)(24,26,29,37)(25,31,33,39)(27,36,28,35)(30,34,32,38)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3159);