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C₂³×#556 #10585929

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

Aliases

Subgroups

37970 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 22 points:

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493125);