Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18252 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18283 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#538 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
886 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(13,19)(20,23)(24,25,28,30)(26,32,34,39)(27,35,37,31)(29,36,38,33);(8,9)(10,13)(11,14)(12,15)(16,20)(17,19)(18,21)(22,23)(24,26,28,34)(25,29,30,38)(27,36,37,33)(31,39,35,32);(8,10)(9,13)(11,16)(12,17)(14,20)(15,19)(18,22)(21,23)(24,25)(26,29)(27,35)(28,30)(31,37)(32,36)(33,39)(34,38);(8,11,12,18)(9,14,15,21)(10,16,17,22)(13,20,19,23)(25,30)(29,38)(31,35)(32,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11271);