Finite Group Databasebeta

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C₂×#1259665 #72324940

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

Aliases

Subgroups

69875 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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