Finite Group Databasebeta

?

← Prev (#85805) Next (#85807) →

C₂×#5572 #85806

• 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)(11,17)(15,23)(16,25)(22,24);(1,2)(10,13,14,21)(11,16,17,25)(12,18,19,20)(15,22,23,24);(10,12,14,19)(11,15,17,23)(13,20,21,18)(16,24,25,22);(4,5)(10,11)(12,15)(13,16)(14,17)(18,22)(19,23)(20,24)(21,25);(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, 18382);