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C₂³×#46367 #72325280

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

Aliases

Subgroups

1462968 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 26 points:

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

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