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C₂×#10777 #353361

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

Aliases

Subgroups

4050 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260557);