Finite Group Databasebeta

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C₂×#712466 #72323890

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

Aliases

Subgroups

42279 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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