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C₂³×#2711 #72339194

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

Aliases

Subgroups

116005 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

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