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C₂×#3174 #60678

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

Aliases

Subgroups

985 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)(13,19)(14,21)(16,22)(18,24)(20,25)(23,26);(4,7)(8,10)(11,12,15,17)(13,16,20,23)(14,18,21,24)(19,22,25,26);(11,13,14,19,15,20,21,25)(12,16,18,22,17,23,24,26);(3,5,6,9)(4,8,7,10)(12,17)(16,23)(18,24)(22,26)

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53666);