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C₂×#2700 #52121

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

Aliases

Subgroups

1425 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 45109);