Finite Group Databasebeta

← Group #289291

Character table — Group #289291

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222222244444444444488888888888888888881616161616161616161632323232
order12224444448888244488888888888888888888888888822444488882488
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1111111111-1-1-11-111-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111111-1-1-1-1-1111-11-1-111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111
χ61111111111111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1111-11-1-1-1-111-1-1
χ71111111111111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-11-1111111-1-1
χ81111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111
χ91111111111-1-1-1-11111-1-1-1-11111-111111111-1-1-1-1-1-1-1-1-1-1111-11-1-1-11-11-11-1
χ101111111111-1-1-1-11111-1-1-1-11111-1111111-1-111-1-1-1-1-1-1-1-11-1-1111-1-1-11-11-11
χ111111111111-1-1-1-11111-1-1-1-11111-111-1-1-1-111-1-1-1-1-1-11111-111-1-1-1111-1-11-11
χ121111111111-1-1-1-11111-1-1-1-11111-111-1-1-1-1-1-111-1-1-1-11111-1-1-11-1111-111-11-1
χ131111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-11-11111-1-111-1
χ141111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-111-1-1-111-111-1-11
χ151111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-1-1111-1-11-11-1-11
χ161111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-11-1-1-1-11-111-1
χ172222222-2-222222-2-22-222-2-20000-200000022220000000000000000-2-20000
χ182222222-2-222222-2-22-222-2-20000-2000000-2-2-2-20000000000000000220000
χ192222222-2-22-2-2-2-2-2-22-2-2-2220000200000022-2-20000000000000000-220000
χ202222222-2-22-2-2-2-2-2-22-2-2-22200002000000-2-22200000000000000002-20000
χ2122222-2-22222222-2-2-22-2-2220000-200000000000000000002-2-20200000000
χ2222222-2-22222222-2-2-22-2-2220000-20000000000000000000-2220-200000000
χ2322222-2-2222-2-2-2-2-2-2-2222-2-20000200000000000000000002-220-200000000
χ2422222-2-2222-2-2-2-2-2-2-2222-2-2000020000000000000000000-22-20200000000
χ2522222-2-2-2-22222222-2-2-2-2-2-22i2i−2i−2i22i−2i000000002i2i−2i−2i000000000000000000
χ2622222-2-2-2-22222222-2-2-2-2-2-2−2i−2i2i2i2−2i2i00000000−2i−2i2i2i000000000000000000
χ2722222-2-2-2-22-2-2-2-222-2-222222i2i−2i−2i-22i−2i00000000−2i−2i2i2i000000000000000000
χ2822222-2-2-2-22-2-2-2-222-2-22222−2i−2i2i2i-2−2i2i000000002i2i−2i−2i000000000000000000
χ292222-22222-20000-22-2-2000022220-2-222-2-20000000000002000-2000000000
χ302222-22222-20000-22-2-2000022220-2-2-2-222000000000000-20002000000000
χ312222-22222-20000-22-2-20000-2-2-2-202222-2-2000000000000-20002000000000
χ322222-22222-20000-22-2-20000-2-2-2-2022-2-2220000000000002000-2000000000
χ332222-2-2-2-2-2-20000-222200002i2i−2i−2i0−2i2i00000000000022-2-20000002i−2i000000
χ342222-2-2-2-2-2-20000-222200002i2i−2i−2i0−2i2i000000000000-2-222000000−2i2i000000
χ352222-2-2-2-2-2-20000-22220000−2i−2i2i2i02i−2i00000000000022-2-2000000−2i2i000000
χ362222-2-2-2-2-2-20000-22220000−2i−2i2i2i02i−2i000000000000-2-2220000002i−2i000000
χ374444-444-4-4-400004-4-4400000000000000000000000000000000000000000
χ384444-4-4-444-400004-44-400000000000000000000000000000000000000000
χ3944-4-40004-402i22i2−2i2−2i20000002i2−2i22i2−2i22i2−2i2000000000002-22-2000000000000000000
χ4044-4-40004-402i22i2−2i2−2i20000002i2−2i2−2i22i2−2i22i200000000000-22-22000000000000000000
χ4144-4-40004-40−2i2−2i22i22i2000000−2i22i22i2−2i22i2−2i200000000000-22-22000000000000000000
χ4244-4-40004-40−2i2−2i22i22i2000000−2i22i2−2i22i2−2i22i2000000000002-22-2000000000000000000
χ4344-4-4000-4402i22i2−2i2−2i2000000−2i22i222−22−222200000000000−2i2i2i−2i000000000000000000
χ4444-4-4000-4402i22i2−2i2−2i2000000−2i22i2−222222−22000000000002i−2i−2i2i000000000000000000
χ4544-4-4000-440−2i2−2i22i22i20000002i2−2i222−22−2222000000000002i−2i−2i2i000000000000000000
χ4644-4-4000-440−2i2−2i22i22i20000002i2−2i2−222222−2200000000000−2i2i2i−2i000000000000000000
χ474-44-404-40002i2−2i22i2−2i200002i2−2i200000000022−2200000000002i−2i2i−2i00000000000000
χ484-44-404-40002i2−2i22i2−2i200002i2−2i2000000000−22220000000000−2i2i−2i2i00000000000000
χ494-44-404-4000−2i22i2−2i22i20000−2i22i200000000022−220000000000−2i2i−2i2i00000000000000
χ504-44-404-4000−2i22i2−2i22i20000−2i22i2000000000−222200000000002i−2i2i−2i00000000000000
χ514-44-40-440002i2−2i22i2−2i20000−2i22i20000000000022−22000000002i−2i−2i2i00000000000000
χ524-44-40-440002i2−2i22i2−2i20000−2i22i200000000000−222200000000−2i2i2i−2i00000000000000
χ534-44-40-44000−2i22i2−2i22i200002i2−2i20000000000022−2200000000−2i2i2i−2i00000000000000
χ544-44-40-44000−2i22i2−2i22i200002i2−2i200000000000−2222000000002i−2i−2i2i00000000000000
χ554-4-44-4000044-4-44000000000000000000022−2222−220000000000000000000000
χ564-4-44-4000044-4-440000000000000000000−2222−22220000000000000000000000
χ574-4-44-400004-444-4000000000000000000022−22−22220000000000000000000000
χ584-4-44-400004-444-40000000000000000000−222222−220000000000000000000000
χ598-8-8880000-80000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).