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C₂×#60147 #10574201

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

Aliases

Subgroups

10620 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481397);