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C₂×#13143 #494890

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

Aliases

Subgroups

844 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402086);