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C₂³×#2566 #72339235

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

Aliases

Subgroups

117637 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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