Finite Group Databasebeta

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C₂×#153472 #72282008

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

Aliases

Subgroups

2228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 18 points:

(1,2);(3,4,8,7)(5,11)(6,10,12,16)(9,17)(13,15)(14,18);(3,5,12,18,4,9,10,17,8,14,6,11,7,15,16,13);(6,12)(10,16)(11,18)(13,17)

Conjugacy classes & character table

64 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((1,2), (3,4,8,7)(5,11)(6,10,12,16)(9,17)(13,15)(14,18), (3,5,12,18,4,9,10,17,8,14,6,11,7,15,16,13), (6,12)(10,16)(11,18)(13,17));