Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C2×C4 |
| direct product | C7×#10675 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ G | |
426 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,11,13)(10,14,15,12)(16,17,21,23,20,18,19,22);(8,10,11,15)(9,12,13,14)(16,18,20,17)(19,22,21,23)(24,25)(26,28)(27,30)(29,31);(16,17,20,18)(19,23,21,22)(25,28)(26,31)(29,30)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3663);