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C₂³×#2818 #72339176

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

Aliases

Subgroups

148701 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

208 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)(12,15)(16,18)(21,25)(23,26), (8,10)(13,17)(16,18)(19,20,22,24)(21,26,25,23), (7,8,9,10)(11,12)(13,16)(14,15)(17,18)(19,20)(21,23)(22,24)(25,26), (7,8)(9,10)(11,13)(12,16)(14,17)(15,18)(19,21)(20,23)(22,25)(24,26), (3,4), (5,6), (1,2)(3,4)(5,6));