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C₂×#10764 #353339

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

Aliases

Subgroups

4114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 260535);