Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #16249 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | C7×#16577 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C7 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
1094 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)(9,11)(12,13,15,17)(14,18,19,16)(20,21,23,25)(22,24,26,27)(28,29,32,31)(30,34,35,33);(20,22,23,26)(21,24,25,27)(28,30)(29,33)(31,34)(32,35);(12,13)(14,16)(15,17)(18,19)(20,22)(21,24)(23,26)(25,27)(28,31,32,29)(30,34,35,33);(8,9)(10,11)(12,14,15,19)(13,16,17,18)(20,21)(22,24)(23,25)(26,27)(28,30)(29,34)(31,33)(32,35)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 9565);