Finite Group Databasebeta

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C₂×#5122 #83746

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 25 points:

(3,4,5)(6,7,8,9)(10,12,14,22,15,20,13,21)(11,16,18,25,19,23,17,24);(1,2)(12,20)(16,23)(21,22)(24,25);(4,5)(10,11,13,17,15,19,14,18)(12,16,21,24,20,23,22,25);(1,2)

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 16322);