Finite Group Databasebeta

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C₂×#1268755 #72297332

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

Aliases

Subgroups

50009 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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