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C₂×#7966 #181190

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

Aliases

Subgroups

1536 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)(21,29,32,33)(22,26)(23,27)(24,28)(25,31,34,30);(3,5,7,15,8,16,6,14)(4,9,10,17,12,18,11,13)(19,21)(20,25,28,34)(22,30)(23,31)(24,32)(26,33,27,29);(3,6,8,7)(4,10,12,11)(5,14,16,15)(9,17,18,13)(19,22,24,23)(20,26,28,27)(21,30,32,31)(25,33,34,29)

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, 88386);