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C₂×#13232 #495199

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

Aliases

Subgroups

1208 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402395);