Finite Group Databasebeta

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C₂×#72261284 #72331249

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

Aliases

Subgroups

At least 10580 conjugacy classes of subgroups; only the 42608 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

332 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((12,14), (11,12)(13,14)(15,16)(17,20)(18,22)(19,21), (7,8)(9,10)(15,17,19,22)(16,20,21,18), (1,2), (4,6)(7,8,9,10)(16,21)(17,22), (15,16)(17,18)(19,21)(20,22), (3,4)(5,6)(7,8)(9,10)(15,18)(16,17)(19,20)(21,22));