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×#25879 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3499 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
1178 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)(10,14)(11,13)(12,15)(16,17,22,26)(18,23,29,40)(19,30,32,43)(20,34,21,25)(24,36,42,33)(27,41,44,47)(28,39,35,38)(31,46,45,37);(8,10,12,11)(9,13,15,14)(16,18)(17,23)(19,31)(20,28)(21,35)(22,29)(24,41)(25,38)(26,40)(27,33)(30,46)(32,45)(34,39)(36,44)(37,43)(42,47);(8,10,12,11)(9,14,15,13)(16,19,20,33,22,32,21,36)(17,24,25,30,26,42,34,43)(18,27,28,45,29,44,35,31)(23,37,38,41,40,46,39,47);(8,11,12,10)(9,14,15,13)(19,32)(24,42)(27,44)(30,43)(31,45)(33,36)(37,46)(41,47)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 18867);