Finite Group Databasebeta

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C₂×#11797100 #72227374

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1704 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 24 points:

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

Conjugacy classes & character table

156 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((20,21)(22,23), (1,2)(19,20,21), (4,8,9,14)(5,11)(6,13)(10,17,16,15)(12,18), (3,4,5,8,6,10,11,15,7,9,12,14,13,16,18,17)(23,24));