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×#18944 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| 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)(9,13)(11,18)(14,20)(15,19)(17,22)(21,23)(24,25)(26,34)(27,30)(28,33)(29,32)(31,37)(35,38)(36,39);(8,9,12,15)(10,14,16,21)(11,19,18,13)(17,23,22,20)(25,30)(27,28)(31,38)(32,33)(34,39)(36,37);(8,10)(9,14)(11,17)(12,16)(13,20)(15,21)(18,22)(19,23)(24,26)(25,31)(27,37)(28,36)(29,35)(30,38)(32,39)(33,34);(10,16)(14,21)(17,22)(20,23)(25,32)(26,35)(30,33)(36,37)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11932);