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C₂×#23751 #6432445

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

Aliases

Subgroups

1926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339641);