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C₂²×#536 #62680

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

Aliases

Subgroups

5703 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

(3,4);(1,2)(3,4);(6,8)(10,14)(11,17)(12,20)(22,24);(9,10,13,14)(11,18,17,15)(12,16,20,21)(19,24,23,22);(5,6)(7,8)(9,11,13,17)(10,15,14,18)(12,19,20,23)(16,22,21,24);(9,12)(10,16)(11,19)(13,20)(14,21)(15,22)(17,23)(18,24)

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, 55668);