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C₂×H(3,𝔽₄) #3526

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

Aliases

Subgroups

704 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 18 points:

(1,2);(4,7)(5,9)(11,12,14,17)(13,16,18,15);(4,7)(8,10)(11,13,14,18)(12,15,17,16);(3,4)(5,8)(6,7)(9,10)(11,13)(12,16)(14,18)(15,17);(3,5)(4,8)(6,9)(7,10)(11,12)(13,16)(14,17)(15,18)

Conjugacy classes & character table

38 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 2258);