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C₂³×#2479 #72325093

• 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:

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

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