Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4×#120 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#36604 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C7×#2543 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
1888 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,13,11)(10,14,12,15)(16,17,20,19)(18,22,23,21)(25,30)(26,31);(8,9,13,11)(10,15,12,14)(16,18,20,23)(17,21,19,22)(24,25)(26,27)(28,31)(29,30);(8,10,13,12)(9,14,11,15)(16,18)(17,22)(19,21)(20,23)(24,26,29,31)(25,27,30,28);(8,11,13,9)(10,14,12,15)(16,19,20,17)(18,22,23,21)(24,27,29,28)(25,26,30,31);(8,12,13,10)(9,15,11,14)(16,18)(17,22)(19,21)(20,23)(24,28,29,27)(25,31,30,26)490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29592);