Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#19591 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3247 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
590 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)(24,25,29,33)(26,30,35,39)(27,32,28,37)(31,36,38,34);(8,10,11,20,13,19,12,18)(9,14,21,22,16,23,15,17)(24,26)(25,30)(27,36)(28,34)(29,35)(31,37)(32,38)(33,39);(8,9)(10,14)(11,21)(12,15)(13,16)(17,18)(19,23)(20,22)(24,26)(25,31)(27,34)(28,36)(29,35)(30,37)(32,39)(33,38);(8,11,13,12)(9,15,16,21)(10,18,19,20)(14,22,23,17)(24,27,29,28)(25,32,33,37)(26,34,35,36)(30,31,39,38)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12579);