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C₂×#17909 #6344614

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

Aliases

Subgroups

1784 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6251810);