Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9239 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | C7×#9240 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #386 |
| commutator | C22×C4 | C22×C4×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| prime radical | C24×C7 | #41 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
452 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,13,17,20)(11,14)(12,15)(16,19,22,23)(18,21)(25,29,31,34)(26,32,33,35);(8,10)(9,13,15,20)(11,16)(12,17)(14,19,21,23)(18,22)(24,25,27,34,28,31,36,29)(26,30,35,38,33,39,32,37);(8,11,12,18)(9,14,15,21)(10,16,17,22)(13,19,20,23)(24,26)(25,30)(27,35)(28,33)(29,37)(31,39)(32,36)(34,38)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2228);