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C₂×#18022 #6344927

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

Aliases

Subgroups

1798 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6252123);