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C₂³×#16255 #72325662

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

Aliases

Subgroups

2915944 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

416 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)(11,12)(13,14)(15,16)(17,18)(19,20)(21,23)(22,24)(25,26), (8,10)(12,14)(16,18)(19,20,22,24)(21,23,26,25), (3,4), (5,6), (8,10)(11,12,13,14)(15,16)(17,18)(19,20)(21,25)(22,24)(23,26), (1,2)(3,4)(5,6), (7,8)(9,10)(11,12)(13,14)(19,21)(20,23)(22,26)(24,25));