Finite Group Databasebeta

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C₂×#5233 #84070

• 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)(13,21)(14,19)(16,25)(17,23)(18,20)(22,24);(1,2)(10,11,14,17)(12,15,19,23)(13,16,20,24)(18,22,21,25);(4,5)(6,7,8,9)(12,18)(13,20)(15,22)(16,24)(19,21)(23,25);(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, 16646);