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C₂³×#536 #10585911

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

Aliases

Subgroups

58818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

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, 10493107);