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C₂×C₄×#546 #7625388

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

Aliases

Subgroups

14346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532584);