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C₂×#12969 #494378

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

Aliases

Subgroups

1091 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401574);