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C₂×#38164 #7635375

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

Aliases

Subgroups

7268 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542571);