Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#23261 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle, prime radical | C23×C7 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
608 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(9,13)(14,15)(16,17)(18,21)(19,23)(20,22)(24,25,30,26,29,32,28,34)(27,31,36,33,37,39,38,35);(8,9)(10,14)(11,15)(12,13)(16,18,20,19)(17,21,22,23)(24,26,30,32,29,34,28,25)(27,35,36,31,37,33,38,39);(8,10,12,11)(9,14,13,15)(16,19,20,18)(17,21,22,23)(24,27,29,37)(25,31,32,39)(26,33,34,35)(28,38,30,36);(8,11,12,10)(9,14,13,15)(24,28,29,30)(25,26,32,34)(27,36,37,38)(31,35,39,33)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16249);