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C₂³×#401 #7627702

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

Aliases

Subgroups

11178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 30 points:

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

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, 7534898);