Finite Group Databasebeta

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C₂×#72219674 #72323278

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

Aliases

Subgroups

At least 11264 conjugacy classes of subgroups; only the 42688 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

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