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C₂×#2862 #36632

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

Aliases

Subgroups

1407 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 29620);