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×#18957 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3547 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
874 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)(8,9,13,17)(10,18,21,22)(11,16,12,15)(14,19,23,20)(26,33)(27,28)(30,37)(31,35)(34,36)(38,39);(8,10,13,21)(9,14,17,23)(11,19,12,20)(15,22,16,18)(24,25)(26,30)(27,31)(28,35)(29,32)(33,38)(34,39)(36,37);(9,15)(11,12)(14,22)(16,17)(18,23)(19,20)(24,26)(25,30)(27,33)(28,36)(29,34)(31,38)(32,39)(35,37);(8,11,13,12)(9,15,17,16)(10,19,21,20)(14,22,23,18)(24,27,29,28)(25,31,32,35)(26,33,34,36)(30,38,39,37)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11945);