Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C7×#62752 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| socle | C22×C7 | C26 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ G | |
6528 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)(10,16)(11,15)(12,14)(13,17)(18,22)(19,21)(20,23)(24,25)(26,29)(27,31)(28,30)(32,37)(33,36)(34,39)(35,38);(8,10)(9,13)(11,18)(12,17)(14,16)(15,20)(19,23)(21,22)(24,26,28,33)(25,29,30,36)(27,34,35,32)(31,39,38,37);(10,17)(13,16)(18,23)(20,22)(25,30)(29,36)(31,38)(37,39);(9,14)(13,16)(15,21)(20,22)(24,27,28,35)(25,31,30,38)(26,32,33,34)(29,37,36,39);(25,30)(29,36)(31,38)(37,39);(8,11,12,19)(9,15,14,21)(10,18,17,23)(13,20,16,22)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55740);