Finite Group Databasebeta

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C₂²×#829 #83871

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 39 points:

(5,6,7)(8,10,13,21)(9,14,17,31)(11,23,26,39)(12,28,24,20)(15,33,34,38)(16,35,27,30)(18,36,37,22)(19,32,29,25);(6,7)(8,9,13,17)(10,18,21,37)(11,22,26,36)(12,27,24,16)(14,29,31,19)(15,32,34,25)(20,38,28,33)(23,35,39,30);(3,4);(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, 16447);