Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #34980 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#35100 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C2×C7×#120 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
1810 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(12,15)(13,14)(17,21)(18,23)(25,28)(29,31);(8,9,12,15)(10,11,14,13)(16,17,20,21)(18,22,23,19)(24,25)(26,29)(27,28)(30,31);(8,10,12,14)(9,13,15,11)(16,18)(17,22)(19,21)(20,23);(8,9)(10,13)(11,14)(12,15);(8,11,12,13)(9,14,15,10)(16,19,20,22)(17,18,21,23)(24,26,27,30)(25,29,28,31)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 28088);