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C₂²×C₄×C₂²⋊Q₈ #7625250

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

Aliases

Subgroups

15026 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532446);