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C₂×#517573 #72339335

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

Aliases

Subgroups

160069 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

256 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)(12,15)(13,17)(21,25)(23,26), (4,6)(7,8,9,10)(13,17)(16,18)(19,20,22,24)(21,26,25,23), (3,4)(5,6)(7,8)(9,10)(11,12)(13,16)(14,15)(17,18), (1,2), (19,21)(20,23)(22,25)(24,26), (11,13)(12,16)(14,17)(15,18)(19,21)(20,23)(22,25)(24,26));