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C₂×#13077 #494667

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

Aliases

Subgroups

1306 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401863);