Finite Group Databasebeta

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C₂×#5751 #87162

• 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:

(3,4,5)(6,8,9,14,10,15,16,20)(7,12,13,19,11,17,18,21);(1,2)(6,7)(8,12)(9,13)(10,11)(14,19)(15,17)(16,18)(20,21);(7,11)(12,17)(13,18)(19,21);(4,5)(8,14)(9,16)(12,19)(13,18)(15,20)(17,21);(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, 19738);