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C₂×#21559 #6372919

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

Aliases

Subgroups

2614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

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, 6280115);