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C₂×#39815 #7637333

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

Aliases

Subgroups

6004 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7544529);