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C₂×#12649 #493081

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

Aliases

Subgroups

1154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400277);