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C₂²×#1337713 #72296983

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

Aliases

Subgroups

At least 6579 conjugacy classes of subgroups; only the 36464 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 32 points:

(5,6)(7,8)(18,21)(22,23)(25,26)(27,30)(28,29)(31,32);(5,6,8,7)(11,15)(14,16)(17,18,20,21)(19,22,24,23)(25,27,29,32)(26,30,28,31);(6,7)(10,13)(14,16)(26,28)(27,32);(6,7)(9,10)(11,14)(12,13)(15,16)(17,18)(19,23)(20,21)(22,24)(25,27)(26,31)(28,30)(29,32);(5,7,8,6)(9,11,12,15)(10,14,13,16)(17,19,20,24)(18,22,21,23)(25,28,29,26)(27,31,32,30);(3,4);(1,2)(3,4)

Conjugacy classes & character table

344 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((5,6)(7,8)(18,21)(22,23)(25,26)(27,30)(28,29)(31,32), (5,6,8,7)(11,15)(14,16)(17,18,20,21)(19,22,24,23)(25,27,29,32)(26,30,28,31), (6,7)(10,13)(14,16)(26,28)(27,32), (6,7)(9,10)(11,14)(12,13)(15,16)(17,18)(19,23)(20,21)(22,24)(25,27)(26,31)(28,30)(29,32), (5,7,8,6)(9,11,12,15)(10,14,13,16)(17,19,20,24)(18,22,21,23)(25,28,29,26)(27,31,32,30), (3,4), (1,2)(3,4));