Finite Group Databasebeta

?

← Prev (#6379186) Next (#6379188) →

C₂×#22458 #6379187

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

Aliases

Subgroups

4636 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6286383);