Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19713 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#19714 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
690 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)(10,17,15,12)(11,14,19,21)(18,23,22,20)(24,25,30,35)(26,36,37,32)(27,39,38,31)(28,34,29,33);(8,10,12,9,13,15,17,16)(11,18,20,14,19,22,23,21)(24,26,28,38,30,37,29,27)(25,31,33,36,35,39,34,32);(8,11)(9,14)(10,18)(12,20)(13,19)(15,22)(16,21)(17,23)(24,27,29,37,30,38,28,26)(25,32,34,39,35,36,33,31);(11,19)(14,21)(18,22)(20,23)(26,37)(27,38)(31,39)(32,36)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12702);