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×#62864 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
6666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 6 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,18)(11,22)(12,16)(13,17)(14,21)(15,24)(19,34)(20,33)(23,37)(25,30)(26,32)(27,38)(28,36)(29,35)(31,39);(8,10,12,21)(9,14,16,18)(11,23,25,19)(13,20,26,36)(15,29,31,27)(17,28,32,33)(22,34,30,37)(24,38,39,35);(8,11,12,25)(9,15,16,31)(10,19,21,23)(13,24,26,39)(14,27,18,29)(17,22,32,30)(20,35,36,38)(28,37,33,34);(9,16)(11,24)(14,18)(15,30)(17,32)(19,35)(22,31)(23,38)(25,39)(27,34)(28,33)(29,37);(10,20)(14,28)(18,33)(19,35)(21,36)(23,38)(27,37)(29,34);(9,17)(14,28)(15,22)(16,32)(18,33)(27,37)(29,34)(30,31)490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55852);