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C₂×#23444 #6431791

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

Aliases

Subgroups

8962 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6338987);