Finite Group Databasebeta

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C₂×#47090 #7700814

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

Aliases

Subgroups

5748 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7608010);