Finite Group Databasebeta

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C₂×#37966 #7635176

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

Aliases

Subgroups

7284 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542372);