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C₂³×#59803 #72300242

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

Aliases

Subgroups

1694392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 26 points:

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

Conjugacy classes & character table

512 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((8,10)(11,12,15,16)(13,17,18,14)(19,20,23,25)(21,22,24,26), (7,8)(9,10)(11,12,15,16)(13,17,18,14), (13,18)(14,17)(19,21)(20,22)(23,24)(25,26), (11,13)(12,14)(15,18)(16,17), (11,14)(12,13)(15,17)(16,18)(19,22)(20,24)(21,25)(23,26), (3,4), (5,6), (1,2)(3,4)(5,6));