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C₂×#4701 #78477

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 21 points:

(3,4,5)(14,15,16,19,17,18,20,21);(1,2)(6,8,9,13)(7,10,11,12)(15,18)(19,21);(4,5)(6,7,9,11)(8,12,13,10);(1,2)

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 11053);