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C₂×#20990 #6371511

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

Aliases

Subgroups

6834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278707);