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C₂×#39146 #7637094

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

Aliases

Subgroups

5890 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7544290);