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C₂×#59827 #7666982

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

Aliases

Subgroups

8278 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7574178);