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×#33867 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C7 |
| prime radical | C7×#3285 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C4×C7×D4 ◁ C7×C8×D4 ◁ G | |
546 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)(18,23)(19,29)(20,32)(21,36)(22,26)(24,30)(25,34)(27,43)(28,42)(31,46)(33,38)(35,45)(37,41)(39,47)(40,44);(8,10)(9,12)(11,15)(13,14)(16,18,22,21)(17,23,26,36)(19,27,31,37)(20,28,35,34)(24,38,40,39)(25,32,42,45)(29,43,46,41)(30,33,44,47);(16,19,22,31)(17,24,26,40)(18,27,21,37)(20,33,35,47)(23,38,36,39)(25,41,42,43)(28,44,34,30)(29,45,46,32);(10,15)(12,14)385 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 26855);