Finite Group Databasebeta

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C₂×#52302 #7633631

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

Aliases

Subgroups

5718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540827);