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D₄×#560 #8091776

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

Aliases

Subgroups

9279 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)(7,14)(8,13)(9,11)(10,16)(12,18)(15,19)(17,20);(5,7)(6,10)(8,16)(9,17)(11,19)(12,20)(13,14)(15,18);(6,11)(7,15)(10,14)(12,13)(16,17)(19,20);(6,12)(7,16)(10,19)(11,13)(14,20)(15,17)

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, 7998972);