Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13402 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#13402 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C2×C7×#472 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ C2×C7×#131 ◁ G | |
404 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(9,15)(10,20)(11,13)(12,26)(16,31)(17,34)(18,19)(21,39)(22,27)(23,37)(24,38)(25,28)(29,32)(33,35);(8,9)(10,21)(11,18)(12,17)(13,15)(14,19)(16,22)(20,35)(23,33)(24,29)(25,36)(26,30)(27,39)(28,34)(31,38)(32,37);(8,10)(9,16,19,33)(11,23)(12,27)(13,22)(14,24)(15,29,18,21)(17,35,34,31)(20,26)(25,38)(28,37)(30,32,36,39)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6390);