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C₂³×#2687 #72325153

• 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:

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

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