Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18618 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18660 |
| 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 | |
908 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)(25,30)(26,34)(27,28)(32,33)(35,36)(37,38);(8,10,12,17)(9,13,14,22)(11,20,21,18)(15,23,19,16)(24,25,29,33)(26,31,35,39)(27,30,28,32)(34,37,36,38);(24,26)(25,31)(27,34)(28,36)(29,35)(30,37)(32,38)(33,39);(9,14)(10,17)(15,19)(18,20)(24,27,29,28)(25,32,33,30)(26,34,35,36)(31,38,39,37)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11648);