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C₂×#15526 #609104

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

Aliases

Subgroups

6126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 516300);