Finite Group Databasebeta

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C₂×#7985555 #72256200

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

Aliases

Subgroups

114567 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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