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C₂×#37644 #7634927

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

Aliases

Subgroups

21478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 18 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7542123);