Finite Group Databasebeta

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C₂×#8070011 #72332212

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

Aliases

Subgroups

At least 6060 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)(7,8)(9,11)(10,12)(13,14);(3,4)(5,6)(7,9)(8,11)(10,13)(12,14)(15,16)(17,20)(18,21)(19,22);(7,8,10,12)(9,11,13,14)(15,17,19,21)(16,20,22,18);(1,2);(8,12)(9,13)(15,17,19,21)(16,18,22,20);(7,8)(9,11)(10,12)(13,14)(15,17)(16,20)(18,22)(19,21);(7,9)(8,11)(10,13)(12,14)(15,18,19,20)(16,21,22,17)

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