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C₂×#2376 #34339

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

Aliases

Subgroups

1435 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,5,6)(8,11)(9,13)(15,16,19,17)(18,21,22,20);(8,11)(12,14)(16,17)(18,22);(7,8)(9,12)(10,11)(13,14)(15,17,19,16)(18,21,22,20);(7,9)(8,12)(10,13)(11,14)(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, 27327);