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C₂×#11129 #357816

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

Aliases

Subgroups

3298 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)(9,16)(10,20)(11,14)(12,15)(13,17)(18,21)(19,22);(7,9,10,17,12,18,11,19)(8,13,14,16,15,22,20,21);(9,17)(10,11)(13,21)(14,20)(16,22)(18,19)

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, 265012);