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C₂³×#2717 #72325227

• 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:

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

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