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C₂×#11131 #357819

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

Aliases

Subgroups

2658 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)(5,15,19,25,18,26,17,10)(6,11,21,29,22,30,23,28)(16,31,20,24,32,27,33,34);(3,5,7,17,9,18,8,19)(4,10,12,15,14,25,13,26)(6,20,21,32,22,33,23,16)(11,27,28,24,30,31,29,34);(3,6)(4,11)(5,16)(7,23)(8,21)(9,22)(10,24)(12,29)(13,28)(14,30)(15,27)(17,33)(18,32)(19,20)(25,34)(26,31)

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, 265015);