Finite Group Databasebeta

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C₂×#5532 #85742

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1240 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)(7,10)(9,12)(11,13)(14,17,18,15)(16,21,20,19);(6,7,9,11)(8,10,12,13)(14,16)(15,19)(17,21)(18,20);(14,15,18,17)(16,21,20,19);(4,5)(8,12)(10,13)(16,20)(19,21);(1,2)

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18318);