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C₂×#18091 #6345136

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

Aliases

Subgroups

1830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6252332);