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C₂×#13307 #498809

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

Aliases

Subgroups

1584 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406005);