Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19230 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#19245 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×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)(8,9,13,16)(10,17,19,22)(11,15,12,21)(14,20,23,18)(24,25)(26,32)(27,29)(28,36)(30,34)(31,35)(33,39)(37,38);(8,10,12,18,13,19,11,20)(9,14,15,17,16,23,21,22)(25,29)(30,38)(31,36)(32,39);(8,9)(10,14)(11,21)(12,15)(13,16)(17,18)(19,23)(20,22)(24,26,27,33)(25,30,29,38)(28,37,35,34)(31,39,36,32);(8,11,13,12)(9,15,16,21)(10,18,19,20)(14,22,23,17)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12233);