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C₂×C₄×#547 #7625390

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

Aliases

Subgroups

12382 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)(13,14,17,18);(12,16)(14,18);(7,8)(9,10)(11,13,15,17)(12,14,16,18);(11,14)(12,17)(13,16)(15,18)

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, 7532586);