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C₂×#20671 #6370824

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

Aliases

Subgroups

4582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278020);