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C₂³×#576 #10586989

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

Aliases

Subgroups

59250 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)(9,13)(10,12)(11,15)(14,18)(16,20)(17,19)(21,22);(8,12)(10,18)(13,19)(14,15)(17,22)(20,21);(7,9)(8,13)(10,17)(11,16)(12,19)(14,21)(15,20)(18,22);(9,16)(13,20)(17,22)(19,21)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10494185);