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C₂×#29271 #6463582

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

Aliases

Subgroups

1700 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6370778);