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C₂×#25749 #6443306

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

Aliases

Subgroups

5656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6350502);