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C₂×#8006 #181318

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

Aliases

Subgroups

1530 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 88514);