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C₂×#36142 #7629769

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

Aliases

Subgroups

8198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536965);