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C₂³×#2521 #72325131

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

Aliases

Subgroups

108381 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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