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C₂×#1866 #20883

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

Aliases

Subgroups

699 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 13871);