Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #36702 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#36750 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C25×C7 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
1778 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)(8,9,12,13)(10,15,14,11)(18,22)(21,23)(24,25)(26,28)(27,30)(29,31);(9,13)(10,14)(17,20)(21,23)(25,26)(29,30);(16,17)(18,21)(19,20)(22,23)(24,26,28,25)(27,30,31,29);(8,10,12,14)(9,11,13,15)(16,17)(18,21)(19,20)(22,23)(24,27,28,31)(25,29,26,30);(8,11)(9,14)(10,13)(12,15)(16,18)(17,21)(19,22)(20,23)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29738);