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C₂×#2564 #34831

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

Aliases

Subgroups

1687 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 27819);