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C₂×#11235 #358047

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265243);