Finite Group Databasebeta

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C₂×#617715 #72323760

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

Aliases

Subgroups

78121 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

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