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C₂×#3196 #60739

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

Aliases

Subgroups

1171 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)(13,17)(14,21)(15,24)(16,19)(18,20)(22,26)(23,25);(3,5)(4,7)(6,10)(8,9)(11,13,16,15)(12,17,19,24)(14,22,23,20)(18,21,26,25);(5,10)(7,9)(11,14,16,23)(12,18,19,26)(13,20,15,22)(17,25,24,21);(4,8)(7,9)

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53727);