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C₂×#11159 #357918

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

Aliases

Subgroups

2498 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)(5,15,17,10,18,26,23,27)(6,19,21,29,22,28,24,11)(16,25,32,30,20,33,31,34);(3,5)(4,10)(6,20)(7,23)(8,17)(9,18)(11,25)(12,26)(13,15)(14,27)(16,22)(19,30)(21,31)(24,32)(28,34)(29,33);(3,6,7,21,9,22,8,24)(4,11,12,28,14,29,13,19)(5,16,17,31,18,20,23,32)(10,25,15,30,27,33,26,34)

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, 265114);