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C₂×#28548 #6466175

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

Aliases

Subgroups

2826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6373371);