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C₂×#3116 #60539

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

Aliases

Subgroups

1075 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)(11,12,16,20)(13,17,23,26)(14,19,15,18)(21,25,22,24);(4,7)(8,10)(11,13,16,23)(12,17,20,26)(14,21,15,22)(18,24,19,25);(12,18)(14,15)(17,24)(19,20)(21,22)(25,26);(3,5,6,9)(4,8,7,10)(11,14,16,15)(12,19,20,18)(13,21,23,22)(17,25,26,24)

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, 53527);