Finite Group Databasebeta

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C₂×#6489 #90477

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 1239);