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C₂×#21184 #6371914

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

Aliases

Subgroups

2558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

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, 6279110);