Finite Group Databasebeta

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C₂×#40006 #7638023

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

Aliases

Subgroups

6688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7545219);