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C₂×#10812 #353516

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

Aliases

Subgroups

1734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 260712);