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C₂×#13201 #495111

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

Aliases

Subgroups

1138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 402307);