Finite Group Databasebeta

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C₂×#122968 #72322842

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

Aliases

Subgroups

739 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(3,4,6,10,8,11,15,12,7,9,14,17,16,18,13,5)(19,20,22,26,24,28,31,29)(21,25,32,34,23,33,30,27);(4,9)(5,12)(10,17)(11,18)(20,25)(21,30)(22,31)(23,32)(26,27)(28,33)(29,34);(3,5,13,18,16,17,14,9,7,12,15,11,8,10,6,4)(19,21,31,30,24,23,22,32)(20,25,29,27,28,33,26,34);(1,2)

Conjugacy classes & character table

160 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((3,4,6,10,8,11,15,12,7,9,14,17,16,18,13,5)(19,20,22,26,24,28,31,29)(21,25,32,34,23,33,30,27), (4,9)(5,12)(10,17)(11,18)(20,25)(21,30)(22,31)(23,32)(26,27)(28,33)(29,34), (3,5,13,18,16,17,14,9,7,12,15,11,8,10,6,4)(19,21,31,30,24,23,22,32)(20,25,29,27,28,33,26,34), (1,2));