Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62862 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C7×#62872 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6502 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 6 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,19)(11,21)(12,16)(13,20)(14,15)(17,22)(18,23)(24,25)(26,32)(27,31)(28,29)(30,34)(33,38)(35,36)(37,39);(9,15)(10,12)(17,21)(18,20)(25,29)(30,32)(31,36)(37,38);(8,10,14,12)(9,16,15,19)(11,18,22,20)(13,17,23,21)(24,25)(26,30)(27,31)(28,29)(32,34)(33,37)(35,36)(38,39);(8,11,14,22)(9,17,15,21)(10,20,12,18)(13,19,23,16)(24,26)(25,30)(27,33)(28,34)(29,32)(31,37)(35,39)(36,38);(8,12,14,10)(9,16,15,19)(11,18,22,20)(13,21,23,17)(24,27,28,35)(25,31,29,36)(26,33,34,39)(30,37,32,38);(8,13)(9,18)(10,17)(11,19)(12,21)(14,23)(15,20)(16,22)490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55860);