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C₂²⋊C₄×C₂²⋊Q₈ #519315

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

Aliases

Subgroups

6330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 20 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 426511);