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C₂×#2932 #60136

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

Aliases

Subgroups

1403 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53124);