Finite Group Databasebeta

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C₂×#5757 #87172

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 19748);