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C₂×#11116 #357782

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

Aliases

Subgroups

2650 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 264978);