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C₂×#5822 #87256

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(3,4,5)(6,8)(7,11)(9,17)(10,15)(12,21)(13,19)(14,16)(18,20);(1,2)(6,7,10,13)(8,11,15,19)(9,12,16,20)(14,18,17,21);(8,15)(11,19)(14,17)(18,21);(4,5)(8,14)(9,16)(11,18)(12,20)(15,17)(19,21);(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, 19832);