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C₂×#27692 #6458218

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

Aliases

Subgroups

1790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6365414);