Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#34421 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator | C22 | C24×C4×C7 |
| Frattini, cosocle | C23 | C25×C7 |
| prime radical | C24×C7 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
1974 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)(8,9,11,10)(12,13)(14,17)(15,19)(16,18)(20,21,25,23)(22,26,30,28)(24,31,32,27)(29,34,35,33);(12,14,16,19)(13,17,18,15)(21,23)(26,28)(27,31)(33,34);(8,10,11,9)(12,14)(13,15)(16,19)(17,18)(20,22,25,30)(21,26,23,28)(24,29,32,35)(27,33,31,34);(12,15)(13,14)(16,17)(18,19)(20,23,25,21)(22,28,30,26)(24,31,32,27)(29,34,35,33);(20,24,25,32)(21,27,23,31)(22,29,30,35)(26,33,28,34)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 27409);