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C₂×#61885 #10578558

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

Aliases

Subgroups

6600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

122 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10485754);