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C₂×#1815 #20676

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

Aliases

Subgroups

687 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 13664);