Finite Group Databasebeta

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C₂×#8077587 #72332223

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

Aliases

Subgroups

At least 10894 conjugacy classes of subgroups; only the 31869 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

190 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((4,6)(16,19)(20,21), (3,4)(5,6)(15,16)(17,20)(18,19)(21,22), (7,8,10,12)(9,11,13,14)(15,16)(17,20)(18,19)(21,22), (1,2), (9,13)(11,14)(16,19)(20,21), (7,8)(9,14)(10,12)(11,13)(15,16)(17,21)(18,19)(20,22), (7,9,10,13)(8,11,12,14)(15,17,18,22)(16,20,19,21));