Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62817 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C7×#62837 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| prime radical | C7×#3444 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6428 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)(8,9,14,19)(10,17,12,15)(11,21,20,16)(13,18,22,23)(26,32)(29,36)(33,38)(37,39);(8,10,14,12)(9,15,19,17)(11,22,20,13)(16,23,21,18)(24,25,28,31)(26,29,32,36)(27,34,35,30)(33,39,38,37);(8,11)(9,16)(10,13)(12,22)(14,20)(15,18)(17,23)(19,21)(24,26)(25,29)(27,33)(28,32)(30,37)(31,36)(34,39)(35,38);(8,12,14,10)(9,17,19,15)(11,22,20,13)(16,23,21,18);(8,13,14,22)(9,18,19,23)(10,20,12,11)(15,21,17,16)(24,27,28,35)(25,30,31,34)(26,33,32,38)(29,37,36,39);(8,9)(10,15)(11,16)(12,17)(13,18)(14,19)(20,21)(22,23)(24,26)(25,29)(27,33)(28,32)(30,37)(31,36)(34,39)(35,38)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55825);