Finite Group Databasebeta

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C₂×#52291 #7633624

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

Aliases

Subgroups

6574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7540820);