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C₂×#61890 #10578566

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

Aliases

Subgroups

7588 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10485762);