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C₂×#28286 #6466031

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

Aliases

Subgroups

2790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6373227);