Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19186 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#19228 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
584 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)(8,9,13,16)(10,17,20,23)(11,15,12,21)(14,18,22,19)(24,25)(26,33)(27,32)(28,30)(29,36)(31,34)(35,39)(37,38);(8,10,12,19,13,20,11,18)(9,14,15,17,16,22,21,23)(25,30)(31,38)(32,36)(33,39);(8,9)(10,14)(11,21)(12,15)(13,16)(17,19)(18,23)(20,22)(24,26)(25,31)(27,34)(28,35)(29,37)(30,38)(32,39)(33,36);(8,11,13,12)(9,15,16,21)(10,18,20,19)(14,17,22,23)(24,27,28,29)(25,32,30,36)(26,34,35,37)(31,39,38,33)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12216);