Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#8135 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C7 | C23 |
| commutator | C23 | C2×C42×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| socle, prime radical | C23×C7 | C2×C42 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C7 ◁ G | |
382 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,12)(14,15)(16,17,19,23,20,22,26,29)(18,21,25,27,24,28,30,31)(32,33)(34,37)(35,39)(36,38)(40,44)(41,43)(42,45)(46,47);(9,12)(13,15)(16,18)(17,21)(19,25)(20,24)(22,28)(23,27)(26,30)(29,31)(32,34,35,40,36,41,42,46)(33,37,39,44,38,43,45,47);(8,10,11,14)(9,13,12,15)(17,22)(18,24)(23,29)(25,30)(33,38)(37,43)(39,45)(44,47)616 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1123);