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C₂×#36112 #7629736

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

Aliases

Subgroups

8274 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536932);