Finite Group Databasebeta

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C₂×#7917829 #72324367

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

Aliases

Subgroups

At least 6830 conjugacy classes of subgroups; only the 31893 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

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