Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9303 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#9306 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #386 |
| commutator | C42 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C7×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
490 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(9,13)(10,11)(14,15)(16,17)(18,22,27,37)(19,29)(20,32)(21,24)(23,30)(25,34)(26,40,41,47)(28,44,43,36)(31,39)(33,38)(35,45,46,42);(8,9,10,14,12,15,11,13)(16,18,21,27)(17,22)(19,26,31,41)(20,28,34,43)(23,35)(24,37)(25,36)(29,40)(30,42,33,45)(32,44)(38,46)(39,47);(8,10,12,11)(9,14,15,13)(16,19,21,31)(17,23,24,38)(18,26,27,41)(20,33,34,30)(22,35,37,46)(25,39,32,29)(28,45,43,42)(36,47,44,40)343 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2294);