Finite Group Databasebeta

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C₂×#5516 #85720

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 25 points:

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

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18296);