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C₂×#61896 #10578570

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

Aliases

Subgroups

6466 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)(21,28)(22,26)(23,31)(24,27)(25,30)(29,34)(32,33);(3,5,8,15)(4,9,12,13)(6,14,7,16)(10,17,11,18)(21,29)(25,33)(28,34)(30,32);(3,6,8,7)(4,10,12,11)(5,14,15,16)(9,17,13,18)(19,21)(20,25)(22,30)(23,32)(24,29)(26,34)(27,33)(28,31);(3,7,8,6)(4,11,12,10)(5,14,15,16)(9,17,13,18);(4,12)(9,13)(10,11)(17,18)(19,22,24,23)(20,26,27,31)(21,30,29,32)(25,34,33,28)

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, 10485766);