Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#23691 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C7×#376 ◁ G | |
796 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7)(8,9,10,11)(12,13)(14,17)(15,16)(18,19)(20,21)(22,25)(23,27)(24,30)(26,28)(29,33)(31,34)(32,35);(13,16)(17,19)(20,22,25,21)(23,31,33,35)(24,30,26,28)(27,32,29,34);(9,11)(20,23,25,33)(21,27,22,29)(24,32,26,34)(28,31,30,35);(12,14,15,18)(13,17,16,19)(20,24,25,26)(21,28,22,30)(23,32,33,34)(27,31,29,35)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16679);