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C₂×#60585 #10575119

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

Aliases

Subgroups

7732 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

122 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482315);