Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19014 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#19049 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3561 | C2 |
| LCS | G ▷ C42 ▷ 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)(8,9,14,19)(10,20,11,22)(12,17,13,18)(15,23,16,21)(24,25,29,27)(26,32,34,39)(28,36,38,31)(30,37,33,35);(8,10,14,11)(9,15,19,16)(12,23,13,21)(17,20,18,22)(24,26,29,34)(25,30,27,33)(28,37,38,35)(31,39,36,32);(8,11,14,10)(9,16,19,15)(12,23,13,21)(17,20,18,22)(24,27,29,25)(26,33,34,30)(28,31,38,36)(32,37,39,35);(8,12,14,13)(9,17,19,18)(10,21,11,23)(15,22,16,20)(26,34)(30,33)(32,39)(35,37)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12037);