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C₂×#55033 #8099384

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

Aliases

Subgroups

6358 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8006580);