Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#26193 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#135 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
734 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)(10,13)(11,15)(12,14)(16,17)(18,29)(19,24)(20,37)(21,27)(22,28)(23,32)(25,36)(26,39)(30,43)(31,40)(33,41)(34,47)(35,44)(38,42)(45,46);(8,10,12,11)(9,13,14,15)(16,18)(17,23)(19,34)(20,31)(21,38)(22,33)(24,43)(25,40)(26,41)(27,29)(28,42)(30,36)(32,39)(35,46)(37,45)(44,47);(8,11,12,10)(9,13,14,15)(16,19,22,20)(17,24,28,37)(18,30,33,46)(21,35,39,36)(23,40,42,47)(25,27,44,26)(29,43,41,45)(31,38,34,32);(16,20,22,19)(17,25,28,44)(18,31,33,34)(21,35,39,36)(23,40,42,47)(24,27,37,26)(29,45,41,43)(30,38,46,32)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 19181);