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C₂×#21004 #6371533

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

Aliases

Subgroups

6142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278729);