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C₂×#36546 #7630248

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

Aliases

Subgroups

10934 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7537444);