Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7035 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#7037 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | #95 |
| commutator | C22×C4 | C42×C7 |
| Frattini, cosocle | C22×C42 | C22×C7 |
| prime radical | C24×C7 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C22×C42×C7 ◁ G | |
476 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 2 generators on 31 points:
(1,2,3,4,5,6,7)(9,13)(10,11)(14,15)(16,17)(18,22)(19,21)(20,23)(25,28,29,30);(8,9,11,14,12,15,10,13)(16,18)(17,20,21,22)(19,23)(24,25)(26,30)(27,29)(28,31)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 25);