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C₂×#13197 #495103

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

Aliases

Subgroups

1144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402299);