Finite Group Databasebeta

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C₂×#7942175 #72298424

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

Aliases

Subgroups

At least 6816 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:

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

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