Finite Group Databasebeta

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C₂²×#1144 #90500

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 27 points:

(5,6,8,10,11,9,7)(12,14,16,22)(13,17,19,26)(15,24,25,21)(18,27,23,20);(6,7)(8,9)(10,11)(12,13,16,19)(14,20,22,27)(15,23,25,18)(17,24,26,21);(3,4);(1,2)

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 1262);