Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D4×D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#33866 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C7 |
| prime radical | C2×C7×D4 | D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C4×C7×D4 ◁ C7×C8×D4 ◁ G | |
548 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)(8,9,11,13)(10,14,15,12)(16,17,21,25)(18,26,29,45)(19,30,34,44)(20,35,32,24)(22,37,39,27)(23,40,42,33)(28,46,36,41)(31,43,47,38);(8,10)(9,12)(11,15)(13,14);(16,18,21,29)(17,22,25,39)(19,31,34,47)(20,36,32,28)(23,41,42,46)(24,43,35,38)(26,44,45,30)(27,40,37,33);(10,15)(12,14)385 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 26854);