Finite Group Databasebeta

?

← Prev (#10574907) Next (#10574909) →

C₂×#60470 #10574908

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

10206 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

(1,2);(4,9)(5,13)(7,19)(11,21)(12,22)(14,27)(15,16)(18,30)(20,24)(26,32)(28,29)(31,34);(3,4,7,9,8,12,19,22)(5,10,15,20,16,25,13,24)(6,11,18,21,17,26,30,32)(14,23,29,31,28,33,27,34);(3,5)(4,10)(6,14)(7,15)(8,16)(9,20)(11,23)(12,25)(13,19)(17,28)(18,29)(21,31)(22,24)(26,33)(27,30)(32,34);(3,6)(4,11)(5,14)(7,18)(8,17)(9,21)(10,23)(12,26)(13,27)(15,29)(16,28)(19,30)(20,31)(22,32)(24,34)(25,33);(6,17)(11,26)(14,28)(18,30)(21,32)(23,33)(27,29)(31,34)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482104);