Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #15257 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | C7×#15935 |
| 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 | |
1082 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)(12,13,16,14)(15,18,19,17)(20,21)(22,25)(23,24)(26,27)(28,29)(30,31)(32,34)(33,35);(13,14)(15,19)(21,23)(25,26)(28,30,32,35)(29,31,34,33);(12,14,16,13)(15,18,19,17)(20,22,24,27)(21,25,23,26)(28,30)(29,33)(31,34)(32,35);(8,9)(10,11)(12,15)(13,17)(14,18)(16,19)(20,23,24,21)(22,26,27,25)(28,31,32,33)(29,30,34,35)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 8923);