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C₂×#36141 #7629768

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

Aliases

Subgroups

9478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536964);