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C₂×#13616 #512689

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

Aliases

Subgroups

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 419885);