Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2215 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C2×C4 |
| direct product | C7×#13285 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C2×D8 |
| commutator | C2×C8 | C22×C4×C7 |
| Frattini, cosocle | C22×C8 | C23×C7 |
| socle | C22×C7 | C2×#102 |
| prime radical | C23×C7 | C2×SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C2×C42×C7 ◁ C2×C4×C7×C8 ◁ G | |
350 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,12)(13,15)(16,17,22,27,23,28,21,38)(18,29,33,45,34,46,32,41)(19,26,20,37,36,40,35,25)(24,39,42,47,43,30,44,31);(9,12)(13,14)(16,18,20,31,22,33,36,39,23,34,35,47,21,32,19,30)(17,24,40,46,38,44,37,45,28,43,26,29,27,42,25,41);(8,10,11,15)(9,13,12,14)(16,19,21,35,23,36,22,20)(17,25,27,26,28,37,38,40)(18,30,32,47,34,39,33,31)(24,41,42,29,43,45,44,46)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6273);