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C₂×#25321 #6447068

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

Aliases

Subgroups

2910 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6354264);