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C₂×#12740 #493534

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

Aliases

Subgroups

3238 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400730);