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C₂×#13319 #498826

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

Aliases

Subgroups

1648 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)(11,18)(12,17)(13,19)(15,22)(16,24)(21,34)(23,35)(25,32)(26,30)(27,31)(28,33)(29,38)(36,37);(3,4)(5,6)(8,14)(10,24)(11,12)(15,29)(16,18)(17,30)(19,31)(20,34)(21,37)(22,28)(25,38)(26,27)(32,35)(33,36);(4,6)(7,9)(8,15)(10,25)(11,28)(12,22)(13,23)(14,29)(16,34)(17,35)(18,20)(19,33)(21,27)(24,38)(26,37)(30,32)(31,36)

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, 406022);