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C₂×#12974 #494394

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

Aliases

Subgroups

1075 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401590);