Finite Group Databasebeta

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C₂²×#11036 #72317026

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

42437 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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