Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7035 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#7045 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | #95 |
| commutator | C22×C4 | C42×C7 |
| Frattini, cosocle | C22×C42 | C22×C7 |
| prime radical | C24×C7 | C4⋊C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C22×C42×C7 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 2 generators on 31 points:
(1,2,3,4,5,6,7)(8,9)(10,12)(11,14)(13,15)(16,17)(18,22)(19,21)(20,23)(24,25,28,26,27,30,29,31);(9,12,14,13)(16,18)(17,20,21,22)(19,23)(24,26,29,30,27,31,28,25)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 33);