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C₂×#28183 #6462909

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

Aliases

Subgroups

2404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6370105);