Finite Group Databasebeta

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C₂×#7992837 #72331537

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

Aliases

Subgroups

At least 10590 conjugacy classes of subgroups; only the 31821 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

184 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((3,4)(5,6)(7,8)(9,12)(10,11)(13,14)(15,16,19,20)(17,21,22,18), (3,4)(5,6)(15,17,19,22)(16,18,20,21), (8,11)(12,13)(15,17)(16,18)(19,22)(20,21), (4,5)(15,17)(16,18)(19,22)(20,21), (1,2), (3,4,6,5)(7,8)(9,13)(10,11)(12,14)(15,18,19,21)(16,17,20,22), (3,5,6,4)(7,9,10,14)(8,12,11,13)(15,17)(16,18)(19,22)(20,21));