Finite Group Databasebeta

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C₂×#6510 #90505

• 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:

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 1267);