Finite Group Databasebeta

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C₂×#519284 #72331260

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

Aliases

Subgroups

67393 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

280 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)(16,20)(18,21), (15,16)(17,21)(18,22)(19,20), (1,2), (4,6)(8,10)(17,22)(18,21), (7,8)(9,10)(15,17,19,22)(16,21,20,18), (3,4)(5,6)(7,8)(9,10)(15,18,19,21)(16,22,20,17));