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C₂×#61808 #10577985

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

Aliases

Subgroups

6510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10485181);