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C₂³×#471 #10574886

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

Aliases

Subgroups

10842 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

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, 10482082);