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C₂×#61107 #10576172

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

Aliases

Subgroups

10254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10483368);