Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#24800 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#135 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
842 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(8,9,10,11)(12,13,17,23)(14,19,27,36)(15,28,31,39)(16,22,32,21)(18,26,34,25)(20,37,40,30)(24,41,29,33)(35,43,38,42);(12,14,16,25,17,27,32,26)(13,18,21,19,23,34,22,36)(15,24,30,42,31,29,37,43)(20,33,28,35,40,41,39,38);(9,11)(12,14)(13,19)(15,29)(16,25)(17,27)(18,22)(20,38)(21,34)(23,36)(24,31)(26,32)(28,33)(30,43)(35,40)(37,42)(39,41);(12,15,16,30,17,31,32,37)(13,20,21,28,23,40,22,39)(14,24,25,42,27,29,26,43)(18,33,19,35,34,41,36,38)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17788);