Finite Group Databasebeta

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C₂×#1258561 #72296331

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

Aliases

Subgroups

45027 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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