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C₂×#20885 #6371329

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

Aliases

Subgroups

4698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278525);