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C₂×#11118 #357785

• 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);(3,4,8,12,9,13,7,23)(5,14,18,25,17,26,16,10)(6,11,21,28,22,30,20,29)(15,31,33,24,32,27,19,34);(3,5,7,16,9,17,8,18)(4,10,12,14,13,25,23,26)(6,19,20,32,22,33,21,15)(11,27,28,34,30,31,29,24);(3,6)(4,11)(5,15)(7,20)(8,21)(9,22)(10,24)(12,28)(13,30)(14,27)(16,19)(17,32)(18,33)(23,29)(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, 264981);