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C₂×#61070 #10576057

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

Aliases

Subgroups

10932 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483253);