Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#7451 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C7 | #357 |
| commutator | C2×C16 | C2×C4×C7 |
| Frattini, cosocle | C4×C16 | C22×C7 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C42×C7 ◁ C4×C7×C8 ◁ C4×C7×C16 ◁ G | |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 2 generators on 47 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(13,15)(16,17,19,25,35,44,47,23,22,28,18,29,21,27,36,41,20,26,33,40,31,42,30,39,38,45,32,24,37,43,34,46);(8,9,11,13)(10,15,14,12)(17,23)(18,30)(19,34)(21,31)(22,38)(24,27)(25,44)(26,39)(28,46)(29,43)(32,47)(33,36)(35,37)(40,42)(41,45)343 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 439);