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×#18911 |
| 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 | |
898 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)(26,33)(27,28)(30,37)(31,35)(34,36)(38,39);(8,10,12,17)(9,13,14,22)(11,20,21,18)(15,23,19,16)(24,25)(26,30)(27,31)(28,35)(29,32)(33,38)(34,39)(36,37);(24,26,29,34)(25,30,32,39)(27,33,28,36)(31,38,35,37);(9,14)(10,17)(15,19)(18,20)(24,27,29,28)(25,31,32,35)(26,33,34,36)(30,38,39,37)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11899);