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×#62755 |
| 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 | |
6644 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)(26,30)(27,35)(28,31)(29,32)(33,38)(34,39)(36,37);(8,10)(9,13)(11,18)(12,17)(14,16)(15,20)(19,23)(21,22)(24,26)(25,30)(27,33)(28,36)(29,34)(31,37)(32,39)(35,38);(10,17)(13,16)(18,23)(20,22)(24,27,29,28)(25,31,32,35)(26,33,34,36)(30,37,39,38);(9,14)(13,16)(15,21)(20,22)(24,28,29,27)(25,31,32,35)(26,33,34,36)(30,38,39,37);(25,32)(30,39)(31,35)(37,38);(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, 55743);