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C₂×#37330 #7634642

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

Aliases

Subgroups

5890 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7541838);