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C₂×#36592 #7630304

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

Aliases

Subgroups

15738 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537500);