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C₂×#37833 #7635185

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

Aliases

Subgroups

17136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542381);