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C₂×#36144 #7629771

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

Aliases

Subgroups

10270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536967);