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C₂×#61740 #10577908

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

Aliases

Subgroups

6836 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)(19,20,23,28)(21,27,24,25)(22,30,31,33)(26,32,34,29);(3,5)(4,8)(6,12)(7,13)(9,15)(10,11)(14,18)(16,17)(19,21,23,24)(20,25,28,27)(22,29,31,32)(26,30,34,33);(3,6,7,14)(4,9,10,16)(5,12,13,18)(8,15,11,17)(19,22)(20,26)(21,29)(23,31)(24,32)(25,30)(27,33)(28,34);(5,13)(8,11)(12,18)(15,17)(19,21,23,24)(20,27,28,25)(22,29,31,32)(26,33,34,30);(4,10)(8,11)(9,16)(15,17)(20,28)(25,27)(26,34)(30,33)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10485104);