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C₂×#62914 #10586256

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

Aliases

Subgroups

37332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 18 points:

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

Conjugacy classes & character table

146 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493452);