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C₂×#42942 #7641607

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

Aliases

Subgroups

9862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7548803);