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C₂×#3170 #60672

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

Aliases

Subgroups

1003 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53660);