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×#7450 |
| 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)(16,17,18,23,28,36,43,34,20,25,29,37,32,40,44,35,21,26,30,38,45,47,46,41,31,39,42,33,19,24,27,22);(8,9,11,13)(10,15,14,12)(17,22)(18,27)(19,28)(20,31)(23,24)(25,41)(26,35)(29,46)(30,44)(32,45)(33,36)(34,39)(37,47)(38,40)(42,43)343 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 438);