Finite Group Databasebeta

?

← Prev (#87248) Next (#87250) →

C₂×#5816 #87249

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1512 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)(10,13,14,21)(11,16,17,20)(12,19,18,24)(15,23,22,25);(1,2)(10,12)(11,15)(13,19)(14,18)(16,23)(17,22)(20,25)(21,24);(10,11,14,17)(12,15,18,22)(13,20,21,16)(19,25,24,23);(4,5)(7,9)(12,18)(15,22)(19,24)(23,25);(1,2)

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 19825);