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×#24930 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3013 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
862 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)(10,12)(11,13)(14,15)(16,17)(18,27)(19,32)(20,22)(21,26)(23,31)(24,33)(25,36)(28,37)(29,44)(30,39)(34,41)(35,40)(38,46)(42,43)(45,47);(8,10,11,14)(9,12,13,15)(17,22)(18,28)(20,36)(24,32)(25,26)(29,43)(30,31)(33,35)(37,39)(40,41)(44,47)(45,46);(9,13)(12,15)(16,18)(17,23)(19,29)(20,30)(21,31)(22,37)(24,38)(25,39)(26,27)(28,36)(32,47)(33,43)(34,45)(35,46)(40,42)(41,44);(16,19,21,34)(17,24,26,40)(18,29,31,45)(20,35,36,33)(22,32,25,41)(23,38,27,42)(28,43,30,46)(37,47,39,44)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17918);