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C₂×#13100 #494753

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

Aliases

Subgroups

2072 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(1,2);(3,4,8,11,9,14,7,13)(5,15,19,31,20,33,18,32)(6,21,16,29,23,12,24,26)(10,25,27,22,28,34,30,17);(3,5,16,25)(4,10,26,31)(6,22,8,18)(7,19,23,17)(9,20,24,34)(11,27,12,15)(13,30,21,33)(14,28,29,32);(4,11)(6,23)(7,8)(10,27)(12,26)(13,14)(15,31)(17,22)(18,19)(21,29)(28,30)(32,33)

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401949);