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C₂×#13391 #499026

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

Aliases

Subgroups

1054 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406222);