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×#62881 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6610 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)(10,14)(11,18)(12,13)(15,19)(16,20)(17,23)(21,22)(24,25,30,32)(26,29,27,31)(28,33,37,39)(34,36,35,38);(10,16)(14,20)(17,22)(21,23)(24,26,30,27)(25,31,32,29)(28,35,37,34)(33,36,39,38);(9,13)(14,20)(15,18)(21,23)(25,32)(26,27)(33,39)(34,35);(8,9)(10,14)(11,15)(12,13)(16,20)(17,21)(18,19)(22,23)(24,27,30,26)(25,29,32,31)(28,35,37,34)(33,36,39,38);(8,10,12,16)(9,14,13,20)(11,17,19,22)(15,21,18,23)(24,28,30,37)(25,33,32,39)(26,34,27,35)(29,36,31,38);(8,11)(9,15)(10,17)(12,19)(13,18)(14,21)(16,22)(20,23)(24,29)(25,26)(27,32)(28,36)(30,31)(33,34)(35,39)(37,38)490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55869);