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×#34469 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator | C22 | C24×C4×C7 |
| Frattini, cosocle | C23 | C25×C7 |
| prime radical | C2×C7×#547 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
2372 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)(12,13,15,17)(14,18,19,16)(20,21,25,23)(22,26,30,28)(24,31,32,27)(29,34,35,33);(12,13,15,17)(14,16,19,18)(21,23)(26,28)(27,31)(33,34);(12,13)(14,16)(15,17)(18,19)(20,22,25,30)(21,26,23,28)(24,29,32,35)(27,33,31,34);(8,10,11,9)(12,14,15,19)(13,16,17,18)(20,23,25,21)(22,28,30,26)(24,31,32,27)(29,34,35,33);(20,24)(21,27)(22,29)(23,31)(25,32)(26,33)(28,34)(30,35)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 27457);