Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#10162 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C7×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
510 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(9,13)(10,16)(11,20)(15,21)(17,22)(18,19)(24,25,28,31)(26,32,33,39)(27,35,36,30)(29,37,38,34);(8,9,12,15)(10,17,19,22)(11,21,20,13)(14,18,23,16)(27,36)(30,35)(32,39)(34,37);(8,10)(9,14)(11,18)(12,19)(13,22)(15,23)(16,20)(17,21)(24,26)(25,29)(27,37)(28,33)(30,39)(31,38)(32,35)(34,36)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3150);