Finite Group Databasebeta

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C₂×#72210511 #72236788

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

Aliases

Subgroups

599500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

248 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((1,2), (3,4)(5,6)(7,8)(9,17)(10,15)(11,14)(12,16)(13,18)(19,21)(20,22), (10,11)(14,15)(17,21)(18,20), (7,9)(8,13,16,22)(10,20)(11,18)(12,19)(14,21,15,17), (4,6), (7,10)(8,14)(9,18)(11,12)(13,21)(15,16)(17,22)(19,20));