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C₂×#42408 #7640854

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

Aliases

Subgroups

5876 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7548050);