Finite Group Databasebeta

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C₂×#5724 #86207

• 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)(11,17)(15,23)(16,25)(22,24);(1,2)(7,9)(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

72 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18783);