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C₂×#20903 #6371368

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

Aliases

Subgroups

6402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278564);