Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24468 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#25927 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#41 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
950 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(8,9,12,15)(10,14,11,13)(16,17,20,25)(18,27,29,23)(19,31,33,43)(21,35,22,26)(24,37,42,34)(28,45,46,41)(30,39,36,40)(32,38,47,44);(8,10,12,11)(9,13,15,14)(16,18,20,29)(17,23,25,27)(19,32,33,47)(21,30,22,36)(24,41,42,45)(26,39,35,40)(28,37,46,34)(31,44,43,38);(8,10,12,11)(9,14,15,13)(16,19,22,37,20,33,21,34)(17,24,35,43,25,42,26,31)(18,28,36,32,29,46,30,47)(23,38,40,45,27,44,39,41);(8,11,12,10)(9,14,15,13)(17,25)(19,33)(23,27)(26,35)(28,46)(32,47)(34,37)(39,40)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 18915);