Finite Group Databasebeta

← Group #499355

Character table — Group #499355

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order122244442222224444448888888844444444888888888888161616161616161616161616161616162244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ91111-1-1-1-11-1-1-1-111-1-1111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-1
χ101111-1-1-1-11-1-1-1-111-1-1111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-1-111
χ111111-1-1-1-11-1-1-1-111-1-1111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-1-111-1-11111-1-1
χ121111-1-1-1-11-1-1-1-111-1-1111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1111-1-111-1-1-1-111
χ131111-1-1-1-11-1-1-1-111-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-111-1-1-1-111-1-111
χ141111-1-1-1-11-1-1-1-111-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-11-1-11111-1-111-1-1
χ151111-1-1-1-11-1-1-1-111-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-11-1-1-11111-1-1-1-111
χ161111-1-1-1-11-1-1-1-111-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1111-1-1-1-11111-1-1
χ1722222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ1922222222-222-2-2-22-2-22-2-22222222200000000-2-2-2-20000000000000000000000002-2-22000000000000
χ2022222222-222-2-2-22-2-22-2-22222222200000000-2-2-2-2000000000000000000000000-222-2000000000000
χ2122222222-222-2-2-22-2-22-2-2-2-2-2-2-2-2-2-20000000022220000000000000000000000000000000000002i−2i2i−2i
χ2222222222-222-2-2-22-2-22-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000000000000000−2i2i−2i2i
χ2322222222-2-2-222-2-2-2-2-2220000000000000000000022-2-222-2-222−2−222−2−222−2−222−2−20000000000000000
χ2422222222-2-2-222-2-2-2-2-2220000000000000000000022-2-222-2-2−2−222−2−222−2−222−2−2220000000000000000
χ2522222222-2-2-222-2-2-2-2-22200000000000000000000-2-222-2-22222−2−222−2−2−2−222−2−2220000000000000000
χ2622222222-2-2-222-2-2-2-2-22200000000000000000000-2-222-2-222−2−222−2−22222−2−222−2−20000000000000000
χ272222-2-2-2-22-2-2-2-222-2-22222222-2-2-2-22222-2-2-2-2-2-222-2-2-2-2222200000000000000000000000000000000
χ282222-2-2-2-22-2-2-2-222-2-22222222-2-2-2-2-2-2-2-22222-2-2222222-2-2-2-200000000000000000000000000000000
χ292222-2-2-2-2-222-2-2-2-222-2220000000000000000000022-2-2-2-22222−2−2−2−22222−2−2−2−2220000000000000000
χ302222-2-2-2-2-222-2-2-2-222-2220000000000000000000022-2-2-2-222−2−22222−2−2−2−22222−2−20000000000000000
χ312222-2-2-2-2-222-2-2-2-222-22200000000000000000000-2-22222-2-222−2−2−2−222−2−22222−2−20000000000000000
χ322222-2-2-2-2-222-2-2-2-222-22200000000000000000000-2-22222-2-2−2−22222−2−222−2−2−2−2220000000000000000
χ332222-2-2-2-2-2-2-222-22222-2-22222-2-2-2-20000000022-2-20000000000000000000000000000000000002i−2i−2i2i
χ342222-2-2-2-2-2-2-222-22222-2-22222-2-2-2-20000000022-2-2000000000000000000000000000000000000−2i2i2i−2i
χ352222-2-2-2-2-2-2-222-22222-2-2-2-2-2-2222200000000-2-22200000000000000000000000022-2-2000000000000
χ362222-2-2-2-2-2-2-222-22222-2-2-2-2-2-2222200000000-2-222000000000000000000000000-2-222000000000000
χ3722-2-222-2-222-22-2-2-22-22-2222-2-222-2-2000000002-22-200000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ3822-2-222-2-222-22-2-2-22-22-2222-2-222-2-2000000002-22-20000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ3922-2-222-2-222-22-2-2-22-22-22-2-222-2-22200000000-22-22000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ4022-2-222-2-222-22-2-2-22-22-22-2-222-2-22200000000-22-2200000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ4122-2-222-2-2-22-2-222-2-2222-222-2-222-2-200000000-22-22000000000000000000000000000000002i−2i2i−2i0000
χ4222-2-222-2-2-22-2-222-2-2222-222-2-222-2-200000000-22-2200000000000000000000000000000000−2i2i−2i2i0000
χ4322-2-222-2-2-22-2-222-2-2222-2-2-222-2-222000000002-22-200000000000000000000000000002i−2i2i−2i00000000
χ4422-2-222-2-2-22-2-222-2-2222-2-2-222-2-222000000002-22-20000000000000000000000000000−2i2i−2i2i00000000
χ4522-2-222-2-2-2-222-222-22-2-220000000022-2-222-2-2000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ4622-2-222-2-2-2-222-222-22-2-220000000022-2-222-2-2000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ4722-2-222-2-2-2-222-222-22-2-2200000000-2-222-2-222000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ4822-2-222-2-2-2-222-222-22-2-2200000000-2-222-2-222000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ4922-2-2-2-2222-22-22-2-2-222-2222-2-2-2-22200000000-222-2000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ5022-2-2-2-2222-22-22-2-2-222-2222-2-2-2-22200000000-222-200000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ5122-2-2-2-2222-22-22-2-2-222-22-2-22222-2-2000000002-2-2200000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ5222-2-2-2-2222-22-22-2-2-222-22-2-22222-2-2000000002-2-220000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ5322-2-2-2-222-22-2-22222-2-2-220000000022-2-2-2-222000000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ5422-2-2-2-222-22-2-22222-2-2-220000000022-2-2-2-222000000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ5522-2-2-2-222-22-2-22222-2-2-2200000000-2-22222-2-2000000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ5622-2-2-2-222-22-2-22222-2-2-2200000000-2-22222-2-2000000000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ5722-2-2-2-222-2-222-22-22-222-222-2-2-2-222000000002-2-2200000000000000000000000000002i−2i−2i2i00000000
χ5822-2-2-2-222-2-222-22-22-222-222-2-2-2-222000000002-2-220000000000000000000000000000−2i2i2i−2i00000000
χ5922-2-2-2-222-2-222-22-22-222-2-2-22222-2-200000000-222-2000000000000000000000000000000002i−2i−2i2i0000
χ6022-2-2-2-222-2-222-22-22-222-2-2-22222-2-200000000-222-200000000000000000000000000000000−2i2i2i−2i0000
χ61444444444-4-4-4-44-444-4-4-4000000000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4444444-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000
χ6344-4-444-4-44-44-44-444-4-44-4000000000000000000000000000000000000000000000000000000000000
χ6444-4-4-4-44444-44-4-44-44-44-4000000000000000000000000000000000000000000000000000000000000
χ654-44-44i−4i4i−4i0000000000002i2−2i22i2−2i222−2222−222-22-22i−2i2i−2i00000022−22002i2−2i200000000000000000000000000000000
χ664-44-44i−4i4i−4i0000000000002i2−2i22i2−2i222−2222−22-22-22−2i2i−2i2i000000−222200−2i22i200000000000000000000000000000000
χ674-44-44i−4i4i−4i000000000000−2i22i2−2i22i2−2222−22222-22-22i−2i2i−2i000000−222200−2i22i200000000000000000000000000000000
χ684-44-44i−4i4i−4i000000000000−2i22i2−2i22i2−2222−2222-22-22−2i2i−2i2i00000022−22002i2−2i200000000000000000000000000000000
χ694-44-4−4i4i−4i4i0000000000002i2−2i22i2−2i2−2222−22222-22-2−2i2i−2i2i000000−2222002i2−2i200000000000000000000000000000000
χ704-44-4−4i4i−4i4i0000000000002i2−2i22i2−2i2−2222−2222-22-222i−2i2i−2i00000022−2200−2i22i200000000000000000000000000000000
χ714-44-4−4i4i−4i4i000000000000−2i22i2−2i22i222−2222−222-22-2−2i2i−2i2i00000022−2200−2i22i200000000000000000000000000000000
χ724-44-4−4i4i−4i4i000000000000−2i22i2−2i22i222−2222−22-22-222i−2i2i−2i000000−2222002i2−2i200000000000000000000000000000000
χ734-4-444i−4i−4i4i0000000000002i2−2i2−2i22i222−22−22222-2-222i−2i−2i2i000022−22002i2−2i20000000000000000000000000000000000
χ744-4-444i−4i−4i4i0000000000002i2−2i2−2i22i222−22−2222-222-2−2i2i2i−2i0000−222200−2i22i20000000000000000000000000000000000
χ754-4-444i−4i−4i4i000000000000−2i22i22i2−2i2−222222−222-2-222i−2i−2i2i0000−222200−2i22i20000000000000000000000000000000000
χ764-4-444i−4i−4i4i000000000000−2i22i22i2−2i2−222222−22-222-2−2i2i2i−2i000022−22002i2−2i20000000000000000000000000000000000
χ774-4-44−4i4i4i−4i0000000000002i2−2i2−2i22i2−222222−222-2-22−2i2i2i−2i0000−2222002i2−2i20000000000000000000000000000000000
χ784-4-44−4i4i4i−4i0000000000002i2−2i2−2i22i2−222222−22-222-22i−2i−2i2i000022−2200−2i22i20000000000000000000000000000000000
χ794-4-44−4i4i4i−4i000000000000−2i22i22i2−2i222−22−22222-2-22−2i2i2i−2i000022−2200−2i22i20000000000000000000000000000000000
χ804-4-44−4i4i4i−4i000000000000−2i22i22i2−2i222−22−2222-222-22i−2i−2i2i0000−2222002i2−2i20000000000000000000000000000000000

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