Finite Group Databasebeta

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C₂×#48442 #7703714

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

Aliases

Subgroups

6396 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7610910);