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C₂×#27418 #6449366

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

Aliases

Subgroups

2472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6356562);