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C₂×#35172 #7628397

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

Aliases

Subgroups

10554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535593);