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C₂³×#359 #7622500

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

Aliases

Subgroups

4130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

(1,2);(3,4);(5,6);(7,8,11,16,13,17,12,27)(9,18,20,34,21,35,28,32)(10,22,24,33,26,37,25,15)(14,23,29,36,31,38,30,19);(7,9)(8,14)(10,23)(11,20)(12,28)(13,21)(15,32)(16,29)(17,31)(18,22)(19,25)(24,36)(26,38)(27,30)(33,34)(35,37)

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, 7529696);