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C₂×#13184 #495068

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

Aliases

Subgroups

702 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

(1,2);(4,6)(7,8)(9,17,19,33)(10,21)(11,14)(12,26)(13,18,28,34)(15,24)(16,25)(20,35,27,31)(22,29,37,32)(23,36)(30,38);(7,9,12,27,11,19,25,20)(8,13,16,32,14,28,26,29)(10,22,24,18,23,37,38,34)(15,31,21,17,30,35,36,33);(3,4,5,6)(8,14)(13,28)(15,30)(16,26)(17,33)(21,36)(29,32)(31,35)

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, 402264);