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C₂×#5132 #83765

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

756 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 16341);