Finite Group Databasebeta

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C₂×#72233554 #72298767

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

Aliases

Subgroups

At least 11242 conjugacy classes of subgroups; only the 45920 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 18 points:

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

Conjugacy classes & character table

356 conjugacy classes. The character table is too large to display.

Relationships

GAP

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

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