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C₂²×D₄×H(5,𝔽₂) #72233741

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

Aliases

Subgroups

885549 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 16 points:

(3,4)(9,10)(11,13)(12,15)(14,16);(1,2)(3,4)(9,11,14,12)(10,15,16,13);(9,10)(11,13)(12,15)(14,16);(9,12,14,11)(10,13,16,15);(9,10)(11,15)(12,13)(14,16);(6,8);(5,6)(7,8);(5,6)(7,8)(9,13)(10,11)(12,16)(14,15)

Conjugacy classes & character table

340 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((3,4)(9,10)(11,13)(12,15)(14,16), (1,2)(3,4)(9,11,14,12)(10,15,16,13), (9,10)(11,13)(12,15)(14,16), (9,12,14,11)(10,13,16,15), (9,10)(11,15)(12,13)(14,16), (6,8), (5,6)(7,8), (5,6)(7,8)(9,13)(10,11)(12,16)(14,15));