Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10238 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#10249 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C22×C7×D4 | D4 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
536 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)(10,14)(11,13)(12,16)(15,19)(17,22)(18,23)(20,21)(24,25,29,33)(26,34,36,39)(27,32,28,31)(30,37,38,35);(9,13)(11,19)(14,22)(15,16)(17,20)(21,23)(24,26)(25,30)(27,37)(28,35)(29,36)(31,39)(32,34)(33,38);(8,10,12,18)(9,14,16,23)(11,20,19,17)(13,21,15,22)(25,31)(27,28)(30,34)(32,33)(35,37)(38,39)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3237);