Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19755 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#19778 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3334 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C42×C7 ◁ G | |
606 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,13,11)(10,16,20,23)(12,21,22,15)(14,18,17,19)(24,25)(26,29)(27,30)(28,32)(31,35)(33,36)(34,38)(37,39);(8,10,13,20)(9,14,11,17)(12,18,22,19)(15,23,21,16)(24,26,28,34)(25,29,32,38)(27,33,35,39)(30,36,31,37);(8,11,13,9)(10,17,20,14)(12,21,22,15)(16,19,23,18)(25,30)(27,35)(29,36)(31,32)(33,39)(37,38);(10,18)(12,22)(14,23)(15,21)(16,17)(19,20)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12766);