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C₂×#7124 #124093

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

Aliases

Subgroups

458 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 26 points:

(1,2);(4,7,8,9)(11,12,14,19,15,18,23,25,16,20,22,26,13,17,21,24);(3,4)(5,9)(6,8)(7,10)(12,17,20,18)(14,22)(19,24,26,25)(21,23)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 31289);