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C₂×#63014 #10586333

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

Aliases

Subgroups

37928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493529);