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C₂×#35536 #7628915

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

Aliases

Subgroups

9810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536111);