Finite Group Databasebeta

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C₂×#7837060 #72300007

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

Aliases

Subgroups

At least 6800 conjugacy classes of subgroups; only the 31901 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

196 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((9,13)(10,12)(15,16)(17,18)(19,22)(20,21), (7,8)(9,12)(10,13)(11,14)(15,17)(16,20)(18,22)(19,21), (4,6)(7,9)(8,12)(10,14)(11,13)(15,17)(16,20)(18,22)(19,21), (3,4)(5,6)(7,9,11,13)(8,10,14,12)(15,17)(16,18)(19,21)(20,22), (7,9)(8,10)(11,13)(12,14)(15,18)(16,21)(17,22)(19,20), (7,10)(8,13)(9,14)(11,12)(15,18)(16,21)(17,22)(19,20), (1,2));