Finite Group Databasebeta

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C₂×#845326 #72295002

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

Aliases

Subgroups

131945 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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