Finite Group Databasebeta

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C₂×#72231160 #72291744

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

Aliases

Subgroups

At least 8712 conjugacy classes of subgroups; only the 38328 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

308 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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