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C₂×#36318 #7629971

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

Aliases

Subgroups

10848 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)(10,11)(12,14)(15,16)(17,20)(18,19)(21,22);(3,4,5,6)(7,9,12,10)(8,13,14,11)(16,19)(20,21);(8,14)(9,10)(15,16)(17,21)(18,19)(20,22);(7,10,12,9)(8,11,14,13)(15,17)(16,20)(18,22)(19,21);(7,11)(8,10)(9,14)(12,13)(15,16)(17,21)(18,19)(20,22)

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, 7537167);