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C₂×#10941 #354106

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

Aliases

Subgroups

2818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 261302);