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C₂×#13019 #494514

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

Aliases

Subgroups

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401710);