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C₂×#11089 #357765

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

Aliases

Subgroups

3750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264961);