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C₂×#13247 #495235

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

Aliases

Subgroups

1106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 402431);