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C₂×#148373 #72309947

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

Aliases

Subgroups

5289 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

136 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)(12,17,19,23)(13,21)(14,22)(15,25)(18,20,26,24), (3,4)(5,6)(7,8,9,10)(12,18,19,26)(13,22)(14,21)(17,20,23,24), (4,6)(11,12,14,24,25,26,22,17,16,19,21,20,15,18,13,23), (1,2));