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C₂×#21747 #6374121

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

Aliases

Subgroups

5494 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 6281317);