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×#18976 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3554 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
866 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)(10,17)(11,14)(12,16)(13,21)(15,19)(18,22)(20,23)(24,25,29,32)(26,34,35,38)(27,30,28,33)(31,36,39,37);(8,10)(9,15)(11,18)(12,19)(13,22)(14,20)(16,23)(17,21)(25,30)(27,28)(31,38)(32,33)(34,39)(36,37);(8,11,14,9)(10,18,20,15)(12,16,13,21)(17,19,23,22)(24,26,29,35)(25,31,32,39)(27,37,28,36)(30,38,33,34);(8,12,14,13)(9,16,11,21)(10,19,20,22)(15,23,18,17)(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, 11964);