Finite Group Databasebeta

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C₂×#1418413 #72294855

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

Aliases

Subgroups

51853 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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