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C₂×#11151 #357910

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

Aliases

Subgroups

2646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265106);