Finite Group Databasebeta

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C₂×#841868 #72302550

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

Aliases

Subgroups

29331 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2)(4,6)(7,8)(9,10)(19,20)(21,24)(22,26)(23,25);(7,8,9,10)(13,17)(16,18)(19,20)(21,24)(22,26)(23,25);(7,8)(9,10)(11,12,15,14)(13,16,17,18)(19,21,23,26)(20,24,25,22);(3,4,5,6)(7,8)(9,10)(20,25)(21,26);(3,4)(5,6)(7,8)(9,10)(11,13)(12,16)(14,18)(15,17)(19,20)(21,24)(22,26)(23,25);(3,4)(5,6)(7,8)(9,10)(11,14,15,12)(13,18,17,16)(19,22,23,24)(20,21,25,26)

Conjugacy classes & character table

196 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)(4,6)(7,8)(9,10)(19,20)(21,24)(22,26)(23,25), (7,8,9,10)(13,17)(16,18)(19,20)(21,24)(22,26)(23,25), (7,8)(9,10)(11,12,15,14)(13,16,17,18)(19,21,23,26)(20,24,25,22), (3,4,5,6)(7,8)(9,10)(20,25)(21,26), (3,4)(5,6)(7,8)(9,10)(11,13)(12,16)(14,18)(15,17)(19,20)(21,24)(22,26)(23,25), (3,4)(5,6)(7,8)(9,10)(11,14,15,12)(13,18,17,16)(19,22,23,24)(20,21,25,26));