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C₂×#37666 #7635076

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

Aliases

Subgroups

9418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7542272);