Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#20516 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C7×C8 | C23 |
| commutator | C22 | C22×C42×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle, prime radical | C23×C7 | C23×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7×C8 ◁ G | |
886 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7)(12,13)(14,18)(15,19)(16,17)(20,21,23,27,24,25,30,32)(22,26,28,33,29,31,34,35);(8,9,11,10)(13,17)(18,19);(8,10,11,9)(12,14,16,15)(13,18,17,19)(21,25)(26,31)(27,32)(33,35);(12,15,16,14)(13,19,17,18)(20,22,23,28,24,29,30,34)(21,26,27,33,25,31,32,35)784 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13504);