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C₂×#13099 #494747

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

Aliases

Subgroups

2064 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401943);