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C₂²×C₄×D₇ #6543

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 15 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(224, 175);