Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#23674 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C22×C7 | C2×#121 |
| prime radical | C24×C7 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C23×C4×C7 ◁ G | |
766 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)(10,15)(11,13)(12,14)(16,17,20,25,22,27,21,26)(18,23,29,38,30,39,36,43)(19,31,34,42,35,41,33,24)(28,40,32,46,45,47,44,37);(8,10,12,11)(9,13,14,15)(16,18)(17,23)(19,32)(20,29)(21,36)(22,30)(24,40)(25,38)(26,43)(27,39)(28,33)(31,46)(34,45)(35,44)(37,41)(42,47);(8,11,12,10)(9,13,14,15)(16,19)(17,24)(18,28)(20,33)(21,34)(22,35)(23,37)(25,41)(26,31)(27,42)(29,44)(30,45)(32,36)(38,47)(39,46)(40,43);(16,20,22,21)(17,25,27,26)(18,29,30,36)(19,33,35,34)(23,38,39,43)(24,41,42,31)(28,44,45,32)(37,47,46,40)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16662);