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C₂×#23881 #6437470

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

Aliases

Subgroups

6170 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344666);