Finite Group Databasebeta

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C₂×#7854849 #72280701

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

Aliases

Subgroups

At least 7180 conjugacy classes of subgroups; only the 32013 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

202 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((4,5)(8,12)(13,14)(16,21)(17,22), (3,4,6,5)(8,12)(9,10)(15,16,20,21)(17,18,22,19), (4,5)(7,8,11,12)(9,13,10,14)(15,16,20,21)(17,19,22,18), (3,5,6,4)(8,12)(13,14)(15,17,20,22)(16,18,21,19), (7,8)(9,14)(10,13)(11,12)(15,17)(16,18)(19,21)(20,22), (1,2)(7,9,11,10)(8,13,12,14)(15,18,20,19)(16,17,21,22), (7,10,11,9)(8,14,12,13)(15,19,20,18)(16,22,21,17));