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C₂×#2706 #52127

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

Aliases

Subgroups

1577 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 45115);