Finite Group Databasebeta

← Group #281024

Character table — Group #281024

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888224444444488888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111111-111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111-11-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-11111-1-1-1-11-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-11111-1-1-1-1-1111-1-111-1-1-11
χ172222222222-2-22-2-2222222222-20000-200000000-2-2-2-200000000222200000000000000-2-20000000000
χ182222222222-2-22-2-2222222222-20000-200000000-2-2-2-200000000-2-2-2-200000000000000220000000000
χ192222222222-2-22-2-22-2-2-2-2-2-2-2-2-20000-20000000022220000000022-2-200000000000000-220000000000
χ202222222222-2-22-2-22-2-2-2-2-2-2-2-2-20000-200000000222200000000-2-222000000000000002-20000000000
χ2122222222-2-222-222-200000000-22222-22222-2-2-2-2000000000000000022-2-2-2-200000000000000000000
χ2222222222-2-222-222-200000000-22222-2-2-2-2-222220000000000000000-2-222-2-200000000000000000000
χ2322222222-2-222-222-200000000-2-2-2-2-2-22222-2-2-2-20000000000000000-2-2222200000000000000000000
χ2422222222-2-222-222-200000000-2-2-2-2-2-2-2-2-2-22222000000000000000022-2-22200000000000000000000
χ252222-2-2-2-22200-200-22222-2-2-2-200000022−2−222−2−200002222−2−2−2−22-22-2000000000000000000002−22−200
χ262222-2-2-2-22200-200-22222-2-2-2-200000022−2−222−2−200002222−2−2−2−2-22-2200000000000000000000−22−2200
χ272222-2-2-2-22200-200-22222-2-2-2-2000000−2−222−2−2220000−2−2−2−222222-22-200000000000000000000−22−2200
χ282222-2-2-2-22200-200-22222-2-2-2-2000000−2−222−2−2220000−2−2−2−22222-22-22000000000000000000002−22−200
χ292222-2-2-2-22200-200-2-2-2-2-2222200000022−2−222−2−20000−2−2−2−222222-2-22000000000000000000002−2−2200
χ302222-2-2-2-22200-200-2-2-2-2-2222200000022−2−222−2−20000−2−2−2−22222-222-200000000000000000000−222−200
χ312222-2-2-2-22200-200-2-2-2-2-22222000000−2−222−2−22200002222−2−2−2−22-2-2200000000000000000000−222−200
χ322222-2-2-2-22200-200-2-2-2-2-22222000000−2−222−2−22200002222−2−2−2−2-222-2000000000000000000002−2−2200
χ3322-2-22-22-2002-202-20i2i2−i2−i2i2i2−i2−i2022-2-2000002i−2i2i−2ii2i2−i2−i222−2−222−2−20000002i−2i00i2i2−i2−i222−2−2000000000000
χ3422-2-22-22-2002-202-20i2i2−i2−i2i2i2−i2−i2022-2-200000−2i2i−2i2ii2i2−i2−i2−2−222−2−222000000−2i2i00i2i2−i2−i2−2−222000000000000
χ3522-2-22-22-2002-202-20i2i2−i2−i2i2i2−i2−i20-2-222000002i−2i2i−2ii2i2−i2−i222−2−222−2−2000000−2i2i00−i2−i2i2i2−2−222000000000000
χ3622-2-22-22-2002-202-20i2i2−i2−i2i2i2−i2−i20-2-22200000−2i2i−2i2ii2i2−i2−i2−2−222−2−2220000002i−2i00−i2−i2i2i222−2−2000000000000
χ3722-2-22-22-2002-202-20−i2−i2i2i2−i2−i2i2i2022-2-2000002i−2i2i−2i−i2−i2i2i2−2−222−2−2220000002i−2i00−i2−i2i2i2−2−222000000000000
χ3822-2-22-22-2002-202-20−i2−i2i2i2−i2−i2i2i2022-2-200000−2i2i−2i2i−i2−i2i2i222−2−222−2−2000000−2i2i00−i2−i2i2i222−2−2000000000000
χ3922-2-22-22-2002-202-20−i2−i2i2i2−i2−i2i2i20-2-222000002i−2i2i−2i−i2−i2i2i2−2−222−2−222000000−2i2i00i2i2−i2−i222−2−2000000000000
χ4022-2-22-22-2002-202-20−i2−i2i2i2−i2−i2i2i20-2-22200000−2i2i−2i2i−i2−i2i2i222−2−222−2−20000002i−2i00i2i2−i2−i2−2−222000000000000
χ412-22-22-2-2200-2202-20i2−i2i2−i2i2−i2i2−i202i−2i2i−2i02i−2i2i−2i0000i2−i2i2−i22−22−22−22−200002-200002−22−2i2−i2i2−i2000000000000
χ422-22-22-2-2200-2202-20i2−i2i2−i2i2−i2i2−i202i−2i2i−2i0−2i2i−2i2i0000i2−i2i2−i2−22−22−22−220000-2200002−22−2−i2i2−i2i2000000000000
χ432-22-22-2-2200-2202-20i2−i2i2−i2i2−i2i2−i20−2i2i−2i2i02i−2i2i−2i0000i2−i2i2−i22−22−22−22−20000-220000−22−22−i2i2−i2i2000000000000
χ442-22-22-2-2200-2202-20i2−i2i2−i2i2−i2i2−i20−2i2i−2i2i0−2i2i−2i2i0000i2−i2i2−i2−22−22−22−2200002-20000−22−22i2−i2i2−i2000000000000
χ452-22-22-2-2200-2202-20−i2i2−i2i2−i2i2−i2i202i−2i2i−2i02i−2i2i−2i0000−i2i2−i2i2−22−22−22−2200002-20000−22−22−i2i2−i2i2000000000000
χ462-22-22-2-2200-2202-20−i2i2−i2i2−i2i2−i2i202i−2i2i−2i0−2i2i−2i2i0000−i2i2−i2i22−22−22−22−20000-220000−22−22i2−i2i2−i2000000000000
χ472-22-22-2-2200-2202-20−i2i2−i2i2−i2i2−i2i20−2i2i−2i2i02i−2i2i−2i0000−i2i2−i2i2−22−22−22−220000-2200002−22−2i2−i2i2−i2000000000000
χ482-22-22-2-2200-2202-20−i2i2−i2i2−i2i2−i2i20−2i2i−2i2i0−2i2i−2i2i0000−i2i2−i2i22−22−22−22−200002-200002−22−2−i2i2−i2i2000000000000
χ492-2-2222-2-22-2-2-2222-200000000-22i−2i−2i2i20000000000002-2-222-2-22000000002i−2i00002i−2i−2i2i000000000000
χ502-2-2222-2-22-2-2-2222-200000000-22i−2i−2i2i2000000000000-222-2-222-2000000002i−2i0000−2i2i2i−2i000000000000
χ512-2-2222-2-22-2-2-2222-200000000-2−2i2i2i−2i20000000000002-2-222-2-2200000000−2i2i0000−2i2i2i−2i000000000000
χ522-2-2222-2-22-2-2-2222-200000000-2−2i2i2i−2i2000000000000-222-2-222-200000000−2i2i00002i−2i−2i2i000000000000
χ532-2-2222-2-2-2222-2-2-222-2-222-2-22-20000200000000-222-200000000000000000000000000002i−2i2i−2i000000
χ542-2-2222-2-2-2222-2-2-222-2-222-2-22-20000200000000-222-20000000000000000000000000000−2i2i−2i2i000000
χ552-2-2222-2-2-2222-2-2-22-222-2-222-2-200002000000002-2-2200000000000000000000000000002i−2i−2i2i000000
χ562-2-2222-2-2-2222-2-2-22-222-2-222-2-200002000000002-2-220000000000000000000000000000−2i2i2i−2i000000
χ572-2-2222-2-2-22-2-2-22222-2-222-2-2222i−2i−2i2i-2000000002-2-220000000000000000−2i2i−2i2i2i−2i0000000000000000
χ582-2-2222-2-2-22-2-2-22222-2-222-2-222−2i2i2i−2i-2000000002-2-2200000000000000002i−2i2i−2i−2i2i0000000000000000
χ592-2-2222-2-2-22-2-2-2222-222-2-222-222i−2i−2i2i-200000000-222-20000000000000000−2i2i2i−2i−2i2i0000000000000000
χ602-2-2222-2-2-22-2-2-2222-222-2-222-22−2i2i2i−2i-200000000-222-200000000000000002i−2i−2i2i2i−2i0000000000000000
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-4004004000000000000002222−22−22−22−222222000000000000000000000000000000000000000000
χ634444-4-4-4-4-4-400400400000000000000−22−2222222222−22−22000000000000000000000000000000000000000000
χ6444-4-44-44-400-440-4402i22i2−2i2−2i22i22i2−2i2−2i200000000000000−2i2−2i22i22i200000000000000000000000000000000000000
χ6544-4-44-44-400-440-440−2i2−2i22i22i2−2i2−2i22i22i2000000000000002i22i2−2i2−2i200000000000000000000000000000000000000
χ6644-4-4-44-44000000002i22i2−2i2−2i2−2i2−2i22i22i200000000002i2−2i2−2i22i2000022-2-2-2-222000000000000000000000000000000
χ6744-4-4-44-44000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000−2i22i22i2−2i20000-2-22222-2-2000000000000000000000000000000
χ6844-4-4-44-4400000000−2i2−2i22i22i22i22i2−2i2−2i200000000002i2−2i2−2i22i20000-2-22222-2-2000000000000000000000000000000
χ6944-4-4-44-4400000000−2i2−2i22i22i22i22i2−2i2−2i20000000000−2i22i22i2−2i2000022-2-2-2-222000000000000000000000000000000
χ704-44-44-4-44004-40-4402i2−2i22i2−2i22i2−2i22i2−2i200000000000000−2i22i2−2i22i200000000000000000000000000000000000000
χ714-44-44-4-44004-40-440−2i22i2−2i22i2−2i22i2−2i22i2000000000000002i2−2i22i2−2i200000000000000000000000000000000000000
χ724-44-4-444-4000000002i2−2i22i2−2i2−2i22i2−2i22i20000002i2−2i2−2i22i2000000002-22-2-22-22000000000000000000000000000000
χ734-44-4-444-4000000002i2−2i22i2−2i2−2i22i2−2i22i2000000−2i22i22i2−2i200000000-22-222-22-2000000000000000000000000000000
χ744-44-4-444-400000000−2i22i2−2i22i22i2−2i22i2−2i20000002i2−2i2−2i22i200000000-22-222-22-2000000000000000000000000000000
χ754-44-4-444-400000000−2i22i2−2i22i22i2−2i22i2−2i2000000−2i22i22i2−2i2000000002-22-2-22-22000000000000000000000000000000
χ764-4-4444-4-44-4444-4-4-40000000040000-400000000000000000000000000000000000000000000000000
χ774-4-44-4-4444-400-40040000000000000000000000000022−22−2222−222222−22000000000000000000000000000000
χ784-4-44-4-4444-400-400400000000000000000000000000−222222−2222−22−2222000000000000000000000000000000
χ794-4-44-4-444-4400400-44-4-44-444-400000000000000000000000000000000000000000000000000000000
χ804-4-44-4-444-4400400-4-444-44-4-4400000000000000000000000000000000000000000000000000000000

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