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C₂×#3499 #62802

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

Aliases

Subgroups

5563 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

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, 55790);