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C₂×#18070 #6345110

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

Aliases

Subgroups

1688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6252306);