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C₂×#2717 #52140

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

Aliases

Subgroups

1447 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 45128);