Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7654 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C4 |
| direct product | C7×#7673 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C43×C7 ◁ G | |
384 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(13,15)(17,21,22,23)(24,25,27,31,28,30,36,38)(26,32,34,39,33,29,35,37);(8,9,11,13)(10,15,14,12)(16,17)(18,21)(19,23)(20,22)(24,26,28,33)(25,29,30,32)(27,35,36,34)(31,39,38,37);(16,18,20,19)(17,21,22,23)(26,33)(29,32)(34,35)(37,39)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 661);