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C₂×#12676 #493150

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

Aliases

Subgroups

738 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400346);