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C₂³×#2633 #72325137

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

Aliases

Subgroups

111413 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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