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C₂×#43001 #7667131

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

Aliases

Subgroups

16654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7574327);