Finite Group Databasebeta

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C₂×#1393546 #72296382

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

Aliases

Subgroups

74829 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

172 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((19,20)(21,22)(23,24)(25,26), (7,8)(9,10)(13,17)(16,18)(20,24)(22,26), (3,4,5,6)(7,8,9,10)(12,15)(16,18)(21,25)(22,26), (7,8)(9,10)(11,12)(13,18)(14,15)(16,17)(19,21)(20,22)(23,25)(24,26), (3,4)(5,6)(7,8)(9,10)(11,13)(12,16)(14,17)(15,18)(19,22)(20,25)(21,24)(23,26), (1,2));