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C₂×#10741 #353419

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

Aliases

Subgroups

4066 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)(10,14)(11,23)(12,16)(13,19)(15,25)(18,33)(20,32)(21,30)(22,29)(24,28)(26,34)(27,37)(31,35)(36,38);(7,9)(8,13,16,27)(10,18)(11,19)(12,20)(14,26,29,38)(15,17,23,32)(21,34)(22,35)(24,36)(25,37)(28,33,30,31);(7,10,12,22)(8,14,16,29)(9,18,20,35)(11,24,25,21)(13,26,27,38)(15,30,23,28)(17,31,32,33)(19,36,37,34)

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, 260615);