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×#34463 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator | C22 | C24×C4×C7 |
| Frattini, cosocle | C23 | C25×C7 |
| prime radical | C22×C7×D4 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
2040 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)(13,16)(14,18)(20,21,26,24)(22,29,23,27)(25,32,33,28)(30,34,31,35);(13,16)(17,19)(20,22,26,23)(21,27,24,29)(25,30,33,31)(28,34,32,35);(12,13)(14,17)(15,16)(18,19)(20,23,26,22)(21,27,24,29)(25,31,33,30)(28,34,32,35);(8,10,11,9)(12,14)(13,17)(15,18)(16,19)(20,24,26,21)(22,27,23,29)(25,32,33,28)(30,34,31,35);(20,25,26,33)(21,28,24,32)(22,30,23,31)(27,34,29,35)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 27451);