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C₂×#10743 #353423

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

Aliases

Subgroups

4134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 260619);