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C₂×#61974 #10578765

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

Aliases

Subgroups

6976 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10485961);