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C₂×#18208 #6346478

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

Aliases

Subgroups

3210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6253674);