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C₂×#35522 #7628900

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

Aliases

Subgroups

9928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(7,8)(9,11)(10,13)(12,14);(7,9,12,10)(8,13,14,11)(15,16)(17,18)(19,20)(21,22);(3,4)(5,6)(8,14)(9,10)(16,20)(17,21);(7,10,12,9)(8,13,14,11)(15,17,19,21)(16,18,20,22);(7,11,12,13)(8,9,14,10)(15,18)(16,21)(17,20)(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, 7536096);