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C₂×#21780 #6374192

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

Aliases

Subgroups

4268 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6281388);