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C₂³×#2622 #72291556

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

Aliases

Subgroups

221965 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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