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C₂×#36147 #7629775

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

Aliases

Subgroups

11018 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536971);