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C₂×#13341 #498864

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

Aliases

Subgroups

1694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406060);