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C₂³×#2813 #72325246

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

Aliases

Subgroups

131821 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

208 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)(11,12,14,16)(13,15,17,18)(19,20,23,24)(21,25,26,22), (7,8,9,10)(13,17)(15,18)(20,24)(22,25), (3,4), (5,6), (1,2)(3,4)(5,6), (7,8)(9,10)(11,12)(13,18)(14,16)(15,17)(19,21)(20,22)(23,26)(24,25), (7,8)(9,10)(11,13,14,17)(12,15,16,18)(19,22)(20,21)(23,25)(24,26));