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C₂³×#2710 #72325129

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

Aliases

Subgroups

120101 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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