Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#36700 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| socle | C23×C7 | C25 |
| prime radical | C24×C7 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
1356 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,15)(12,14)(16,17)(18,22)(19,23)(20,21)(24,27)(25,29)(26,28)(30,31)(32,33,36,39)(34,37,41,45)(35,38,43,47)(40,44,42,46);(8,10,12,11)(9,13,14,15)(17,21)(22,27)(23,28)(29,31)(32,34,36,41)(33,37,39,45)(35,42,43,40)(38,46,47,44);(9,14)(13,15)(16,18)(17,22)(19,25)(20,24)(21,27)(23,29)(26,30)(28,31)(32,35)(33,38)(34,40)(36,43)(37,44)(39,47)(41,42)(45,46);(8,11,12,10)(9,15,14,13)(18,24)(22,27)(25,30)(29,31)(33,39)(35,43)(37,45)(40,42);(16,19,20,26)(17,23,21,28)(18,25,24,30)(22,29,27,31)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29688);