Finite Group Databasebeta

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C₂×#61401 #10576687

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

Aliases

Subgroups

7036 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2);(4,8)(9,10)(11,12)(13,20)(14,18)(15,23)(16,19)(17,22)(21,26)(24,25);(3,4,7,8)(5,9,6,10)(13,21)(17,25)(20,26)(22,24);(3,5,7,6)(4,9,8,10)(11,13)(12,17)(14,22)(15,24)(16,21)(18,26)(19,25)(20,23);(3,6,7,5)(4,9,8,10);(11,14,16,15)(12,18,19,23)(13,22,21,24)(17,26,25,20)

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, 10483883);