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C₂×#13209 #495129

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

Aliases

Subgroups

1318 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 402325);