Finite Group Databasebeta

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C₂×#7694192 #72298906

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

Aliases

Subgroups

At least 6648 conjugacy classes of subgroups; only the 32325 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

214 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)(8,11)(12,13)(15,16,18,19)(17,21,22,20), (3,4)(5,6)(7,8)(9,12)(10,11)(13,14)(16,19)(20,21), (3,4)(5,6)(7,8)(9,13)(10,11)(12,14)(15,17)(16,20)(18,22)(19,21), (7,8,10,11)(9,13,14,12)(15,16)(17,20)(18,19)(21,22), (7,8)(9,12)(10,11)(13,14), (7,9)(8,12)(10,14)(11,13)(15,16)(17,20)(18,19)(21,22), (1,2));