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C₂×#42430 #7641126

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

Aliases

Subgroups

11852 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7548322);