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C₂×#23878 #6437471

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

Aliases

Subgroups

6510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

(1,2);(7,8)(9,19)(10,14)(11,17)(12,16)(13,18)(15,20)(21,22);(3,4)(5,6)(7,9,13,20)(8,14,18,22)(10,11,21,12)(15,17,19,16);(4,6)(7,10)(8,15)(9,12)(11,20)(13,21)(14,16)(17,22)(18,19);(7,10)(8,15)(9,11)(12,20)(13,21)(14,17)(16,22)(18,19)

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344667);