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C₂×#400 #2394

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

Aliases

Subgroups

302 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 1126);