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C₂×#3200 #60744

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

Aliases

Subgroups

1157 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)(11,12,15,19)(13,16,20,24)(14,17,22,18)(21,23,26,25);(3,5)(4,7)(6,10)(8,9)(11,13,15,20)(12,16,19,24)(14,21,22,26)(17,23,18,25);(5,10)(7,9)(12,17)(14,22)(16,23)(18,19)(21,26)(24,25);(4,8)(7,9)(13,20)(16,24)(21,26)(23,25)

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, 53732);