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C₂³×#2454 #72325374

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

Aliases

Subgroups

117637 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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