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C₂×#2814 #36651

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

Aliases

Subgroups

1337 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 29639);