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C₂×#2370 #34144

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

Aliases

Subgroups

1255 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27132);