Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18866 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18921 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3518 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
864 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)(10,16)(11,19)(12,14)(13,18)(15,21)(17,23)(20,22)(24,25,30,35)(26,36,32,39)(27,37,31,38)(28,33,29,34);(8,10,12,17)(9,13,14,22)(11,20,21,18)(15,23,19,16)(24,26,30,32)(25,31,35,27)(28,38,29,37)(33,36,34,39);(24,27,30,31)(25,32,35,26)(28,36,29,39)(33,38,34,37);(9,14)(10,17)(15,19)(18,20)(24,28,30,29)(25,33,35,34)(26,37,32,38)(27,36,31,39)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11909);