Finite Group Databasebeta

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C₂×#850883 #72324000

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

Aliases

Subgroups

132041 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

184 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)(13,14)(15,16)(17,18), (4,6)(8,10)(20,22)(24,26), (4,6)(7,8)(9,10)(12,16)(14,18)(19,20,23,22)(21,24,25,26), (1,2), (4,6)(11,13)(12,14)(15,17)(16,18)(19,21)(20,24)(22,26)(23,25), (3,4)(5,6)(11,14)(12,17)(13,16)(15,18)(19,22,23,20)(21,24,25,26));