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C₂×#13351 #498895

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

Aliases

Subgroups

2169 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406091);