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C₂×#48458 #7703224

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

Aliases

Subgroups

7300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7610420);