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C₂×#13258 #495262

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

Aliases

Subgroups

1330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 402458);