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C₂×#59189 #7665744

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

Aliases

Subgroups

10088 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7572940);