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C₂×#28746 #6466801

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

Aliases

Subgroups

2694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6373997);