Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C8 · Schur multiplier (H2) = C23 |
| direct product | C7×#7171 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | D8 |
| commutator | C8 | C4×C7×C8 |
| Frattini, cosocle | C2×C4×C8 | C22×C7 |
| socle, prime radical | C23×C7 | #102 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ C2×C42×C7 ◁ C2×C4×C7×C8 ◁ G | |
282 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(12,13,15,18,16,19,14,17)(21,26)(22,30)(23,32)(24,31)(27,28)(29,35)(33,34);(9,11)(13,17,19,18)(20,21,23,27,24,28,22,26,25,29,30,34,31,33,32,35)616 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 159);