Finite Group Databasebeta

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C₂×#61421 #10576718

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

Aliases

Subgroups

7126 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)(13,19)(14,22)(15,17)(16,20)(18,24)(21,26)(23,25);(3,4,7,8)(5,9,6,10)(11,12)(13,16)(14,18)(15,17)(19,20)(21,25)(22,24)(23,26);(3,5,7,6)(4,9,8,10)(11,13,15,21)(12,16,17,25)(14,23,24,20)(18,26,22,19);(3,6,7,5)(4,9,8,10);(12,17)(16,25)(18,22)(19,26)

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483914);