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C₂×#13214 #495138

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

Aliases

Subgroups

1350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402334);