Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9431 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#9431 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #386 |
| commutator | C42 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C7×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
414 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)(9,13)(10,16)(11,19)(15,21)(17,18)(20,22)(24,25)(26,33,34,37)(27,30,35,36)(28,31)(29,32)(38,39);(8,9,11,13,12,15,19,21)(10,14,17,20,18,23,16,22)(24,26,28,36,29,34,38,30)(25,27,31,37,32,35,39,33);(8,10)(9,14)(11,17)(12,18)(13,20)(15,23)(16,19)(21,22)(24,27)(25,30)(26,31)(28,37)(29,35)(32,36)(33,38)(34,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2419);