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C₂×#20420 #6369863

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

Aliases

Subgroups

5090 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6277059);