Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#26922 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C22×C7×D4 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
732 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(8,9,11,12)(10,14,15,13)(16,17,20,25,21,26,36,23)(18,27,30,38,31,41,28,22)(19,32,33,40,35,39,34,24)(29,37,43,46,45,47,44,42);(9,12)(13,14)(16,18,21,31)(17,22,26,38)(19,29,35,45)(20,28,36,30)(23,27,25,41)(24,37,40,47)(32,42,39,46)(33,44,34,43);(17,23)(18,28)(20,36)(24,32)(25,26)(27,41)(29,43)(30,31)(33,34)(39,40)(42,46)(44,45);(8,10,11,15)(9,13,12,14)(16,19,21,35)(17,24,26,40)(18,29,31,45)(20,34,36,33)(22,37,38,47)(23,32,25,39)(27,42,41,46)(28,43,30,44)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 19910);