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C₂×#1838 #20767

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

Aliases

Subgroups

415 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

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, 13755);