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C₂×#10955 #354125

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

Aliases

Subgroups

2810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 261321);