Finite Group Databasebeta

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C₂×#2077553 #72296305

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

Aliases

Subgroups

49617 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

160 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)(8,10)(12,15)(13,17), (7,8)(9,10)(12,15)(16,18)(20,23)(21,25), (12,15)(13,17)(20,23)(24,26), (4,6)(11,12,14,15)(13,18,17,16)(19,20,22,23)(21,26,25,24), (3,4)(5,6)(11,13)(12,16)(14,17)(15,18)(19,21)(20,24)(22,25)(23,26), (1,2));