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C₂×#11110 #357698

• 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)(5,15,18,25,19,29,17,10)(6,20,21,11,23,28,22,27)(16,24,31,34,32,26,33,30);(3,5,7,17,9,19,8,18)(4,10,12,15,14,25,13,29)(6,16,21,31,23,32,22,33)(11,26,20,34,27,24,28,30);(3,6)(4,11)(5,16)(7,21)(8,22)(9,23)(10,24)(12,20)(13,28)(14,27)(15,30)(17,31)(18,33)(19,32)(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, 264894);