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C₂×#20617 #6370744

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

Aliases

Subgroups

17034 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)(9,17)(10,14)(11,23)(12,15)(13,19)(16,26)(18,34)(20,31)(21,32)(22,29)(24,28)(25,30)(27,35)(33,36)(37,38);(7,9)(8,13)(10,18)(11,24)(12,20)(14,27)(15,28)(16,31)(17,23)(19,26)(21,37)(22,36)(25,35)(29,38)(30,33)(32,34);(7,10,12,22)(8,14,15,29)(9,18,20,36)(11,25,26,21)(13,27,28,38)(16,32,23,30)(17,33,31,34)(19,37,24,35);(8,15)(13,28)(14,29)(16,23)(17,31)(27,38)(30,32)(33,34)

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, 6277940);