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C₂³×#563 #10586113

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

Aliases

Subgroups

35266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 30 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493309);