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C₂×#8231 #182768

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

Aliases

Subgroups

1966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 89964);