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C₂×#8518 #187748

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 94944);