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C₂×#12989 #494433

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

Aliases

Subgroups

1314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401629);