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C₂×#13039 #494563

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

Aliases

Subgroups

1314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401759);