Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #36702 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#36745 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
2184 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2,3,4,5,6,7)(9,11)(14,18)(17,19)(20,21)(22,23)(24,28)(25,26)(27,31)(29,30)(32,33)(34,35);(13,16)(17,19)(21,26)(22,27)(28,33)(29,34);(8,9,10,11)(12,13)(14,17)(15,16)(18,19)(20,22,25,27)(21,23,26,31)(24,29,32,34)(28,30,33,35);(12,13)(14,17)(15,16)(18,19)(20,23)(21,27)(22,26)(24,30)(25,31)(28,34)(29,33)(32,35);(12,14)(13,17)(15,18)(16,19)(20,24,25,32)(21,28,26,33)(22,29,27,34)(23,30,31,35)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29733);