Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18930 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18952 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3214 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
880 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)(10,19)(11,16)(12,17)(13,22)(14,18)(15,20)(21,23)(25,30)(26,33)(27,28)(32,36)(34,35)(37,38);(8,10,14,11)(9,15,18,23)(12,20,13,21)(16,22,19,17)(24,25)(26,31)(27,30)(28,36)(29,32)(33,37)(34,38)(35,39);(8,11,14,10)(9,16,18,19)(12,20,13,21)(15,22,23,17)(24,26,29,35)(25,31,32,39)(27,33,28,34)(30,37,36,38);(8,12,14,13)(9,17,18,22)(10,20,11,21)(15,16,23,19)(24,27,29,28)(25,30,32,36)(26,34,35,33)(31,38,39,37)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11940);