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C₂×#8204 #182429

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

Aliases

Subgroups

1566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 89625);