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C₂×#44604 #7668985

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

Aliases

Subgroups

6118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7576181);