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C₂³×#2468 #72325123

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

Aliases

Subgroups

114933 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

304 conjugacy classes. The character table is too large to display.

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