Finite Group Databasebeta

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C₂×#847037 #72325439

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

Aliases

Subgroups

69577 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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