Finite Group Databasebeta

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C₂×#5234 #84073

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

792 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)(11,15)(13,19)(14,18)(16,22)(17,21)(20,24)(23,25);(1,2)(12,18)(15,21)(19,24)(22,25);(4,5)(7,9)(10,11,13,16,14,17,20,23)(12,15,19,22,18,21,24,25);(1,2)

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 16649);