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C₂×C₄×#537 #7625316

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

Aliases

Subgroups

12082 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)(13,17)(14,15)(16,18);(12,15)(16,17);(7,8)(9,10)(11,12)(13,16)(14,15)(17,18);(11,13,14,18)(12,16,15,17)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532512);