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C₂×#25807 #6443282

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

Aliases

Subgroups

5118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6350478);