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C₂×#40642 #7638875

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

Aliases

Subgroups

8642 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)(19,20)(21,22)(23,24)(25,26);(4,7)(8,9)(11,12)(13,17)(14,15)(16,18)(19,21,23,26)(20,22,24,25);(5,10)(8,9)(12,15)(16,17)(19,20,23,24)(21,25,26,22);(3,5,6,10)(4,8,7,9)(11,12)(13,16)(14,15)(17,18)(19,20)(21,22)(23,24)(25,26);(3,4)(5,8)(6,7)(9,10)(11,13)(12,16)(14,18)(15,17)(19,22)(20,21)(23,25)(24,26)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7546071);