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C₂³×#2481 #72339182

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

Aliases

Subgroups

121485 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)(20,24)(22,25);(12,15)(16,18)(19,20,23,24)(21,25,26,22);(7,8,9,10)(11,12,14,15)(13,18,17,16)(19,21,23,26)(20,22,24,25);(3,4);(5,6);(7,8)(9,10)(11,13)(12,16)(14,17)(15,18)(19,22)(20,21)(23,25)(24,26);(1,2)(3,4)(5,6)

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