Finite Group Databasebeta

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C₂×#72232458 #72286919

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

Aliases

Subgroups

2842202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 22 points:

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

Conjugacy classes & character table

344 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((3,4)(5,6)(7,8)(9,10)(12,14), (15,16)(17,20)(18,21)(19,22), (11,12,13,14)(15,17)(16,18)(19,21)(20,22), (1,2), (7,8)(9,10), (4,5)(8,9)(15,17)(16,20)(18,22)(19,21), (3,5,6,4)(7,9,10,8)(15,18,19,20)(16,21,22,17));