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C₂×#61539 #10576882

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

Aliases

Subgroups

7078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10484078);