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C₂×#61979 #10578772

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

Aliases

Subgroups

8272 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10485968);