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C₂×#25744 #6443300

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

Aliases

Subgroups

5486 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6350496);