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C₂×#34437 #7626007

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

Aliases

Subgroups

10314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7533203);