Finite Group Databasebeta

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C₂×#1083663 #72297027

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

Aliases

Subgroups

43687 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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