Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#10185 |
| 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 | |
550 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,13)(12,15)(16,17,22,27)(18,23,30,39)(19,31,33,42)(20,26,21,25)(24,35,41,34)(28,40,44,47)(29,43,36,38)(32,37,45,46);(9,13)(10,11)(14,15)(16,18)(17,23)(19,32)(20,29)(21,36)(22,30)(24,40)(25,38)(26,43)(27,39)(28,35)(31,46)(33,45)(34,44)(37,42)(41,47);(8,10,12,11)(9,14,15,13)(16,19)(17,24)(18,28)(20,35)(21,34)(22,33)(23,37)(25,42)(26,31)(27,41)(29,45)(30,44)(32,36)(38,47)(39,46)(40,43)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3173);