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C₂×#61831 #10578225

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

Aliases

Subgroups

6408 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)(21,28)(22,26)(23,25)(24,29)(27,31)(30,32)(33,34);(3,5,7,13)(4,8,10,11)(6,14,15,12)(9,17,18,16)(19,21,22,29)(20,24,26,28)(23,30,31,34)(25,33,27,32);(20,25)(21,29)(23,31)(24,32)(26,27)(28,33);(3,6,7,15)(4,9,10,18)(5,12,13,14)(8,16,11,17)(21,29)(24,28)(30,34)(32,33);(4,10)(8,11)(9,18)(16,17)(20,26)(24,28)(25,27)(32,33)

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, 10485421);