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×#36742 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C2×C7×#121 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
2038 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2,3,4,5,6,7)(9,11)(14,18)(17,19)(20,21,25,29)(22,27,23,26)(24,32,33,28)(30,34,31,35);(13,16)(17,19)(20,22,25,23)(21,26,29,27)(24,31,33,30)(28,35,32,34);(8,9,10,11)(12,13)(14,17)(15,16)(18,19)(20,23,25,22)(21,27,29,26)(24,31,33,30)(28,35,32,34);(12,13)(14,17)(15,16)(18,19)(20,24,25,33)(21,28,29,32)(22,30,23,31)(26,34,27,35);(12,14)(13,17)(15,18)(16,19)(20,21)(22,26)(23,27)(24,28)(25,29)(30,34)(31,35)(32,33)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29730);