Finite Group Databasebeta

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C₂×#2601293 #72278816

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

Aliases

Subgroups

58291 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

148 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((4,6)(11,12)(13,16)(14,18)(15,17)(19,20)(21,23)(22,24)(25,26), (4,6)(7,8,9,10)(11,13,15,14)(12,16,17,18)(20,21)(22,26), (4,6)(7,8)(9,10)(19,20,23,21)(22,25,26,24), (3,4,5,6)(11,14,15,13)(12,16,17,18)(19,21,23,20)(22,25,26,24), (11,12)(13,18)(14,16)(15,17)(19,22)(20,24)(21,25)(23,26), (1,2));