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C₂×#5819 #87253

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 21 points:

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

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 19829);