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C₂×#13336 #498873

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

Aliases

Subgroups

1684 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406069);