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C₂×#42969 #7641646

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

Aliases

Subgroups

10772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,5,6)(16,18)(21,22);(7,8,11,9)(10,13,14,12)(15,16,20,18)(17,21,19,22);(3,4)(5,6)(8,9)(12,13)(15,17,20,19)(16,21,18,22);(7,9,11,8)(10,13,14,12)(15,18,20,16)(17,21,19,22);(7,10,11,14)(8,12,9,13)(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, 7548842);