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C₂×#12607 #492953

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

Aliases

Subgroups

1386 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400149);