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D₄×H(3,𝔽₄) #8091758

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

Aliases

Subgroups

9875 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 20 points:

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

Conjugacy classes & character table

95 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7998954);