Finite Group Databasebeta

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C₂×#38549 #7636037

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

Aliases

Subgroups

6262 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7543233);