Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18866 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18924 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C23×C7 | #120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
878 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)(9,13)(10,11)(14,15)(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);(8,9,12,15)(10,13,11,14)(16,18,22,30)(17,23,27,38)(19,29,36,44)(20,32,21,31)(24,37,41,43)(25,39,26,28)(33,47,40,42)(34,46,35,45);(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)(9,14,15,13)(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, 11912);