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C₂×#13400 #499057

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

Aliases

Subgroups

1082 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406253);