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C₂×#3487 #62789

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

Aliases

Subgroups

5755 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

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, 55777);