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C₂×#21099 #6371705

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

Aliases

Subgroups

3346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278901);