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C₂×#63012 #10586331

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

Aliases

Subgroups

38650 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)(14,16)(15,18);(3,4)(5,8)(6,9)(7,10)(11,12,14,16)(13,15,18,17);(3,5)(4,7)(6,10)(8,9)(11,12)(13,15)(14,16)(17,18);(11,13)(12,15)(14,18)(16,17);(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, 10493527);