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C₂×#13231 #495195

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

Aliases

Subgroups

1264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 402391);