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C₂×#10771 #353350

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

Aliases

Subgroups

4022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260546);