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C₂×#37655 #7635101

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

Aliases

Subgroups

12270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542297);