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C₈×H(5,𝔽₂) #60303

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

Aliases

Subgroups

1211 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 16 points:

(9,10,11,13,12,14,15,16);(1,2)(3,7)(4,6)(5,8);(1,3)(2,5)(4,8)(6,7);(3,8)(5,7);(2,6)(5,7)

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53291);