Finite Group Databasebeta

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C₂×#72264092 #72331179

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

Aliases

Subgroups

At least 10844 conjugacy classes of subgroups; only the 43776 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

380 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), (7,8)(9,10)(11,12)(13,14)(17,21)(20,22), (7,8)(9,10)(15,16,19,18)(17,22,21,20), (1,2), (4,6)(8,10), (15,17)(16,20)(18,22)(19,21), (3,4)(5,6)(7,8)(9,10)(15,18,19,16)(17,20,21,22));