Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18866 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#18922 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3497 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
1142 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,13)(12,15)(16,17,22,27)(18,28,30,39)(19,33,36,40)(20,26,21,25)(23,32,38,31)(24,34,41,35)(29,43,44,37)(42,45,47,46);(9,13)(10,11)(14,15)(16,18)(17,23)(19,29)(20,32)(21,31)(22,30)(24,37)(25,39)(26,28)(27,38)(33,47)(34,46)(35,45)(36,44)(40,42)(41,43);(16,19,22,36)(17,24,27,41)(18,29,30,44)(20,35,21,34)(23,37,38,43)(25,33,26,40)(28,42,39,47)(31,46,32,45);(8,10,12,11)(9,13,15,14)(18,30)(23,38)(28,39)(29,44)(31,32)(37,43)(42,47)(45,46)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11910);