Finite Group Databasebeta

← Group #415120

Character table — Group #415120

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12224444222222444444888888884444444488888888888822444444888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1
χ17222222222-2-22-2-22-2-2-22-2222222220000000000000000-2-2-2-20000000000000000000000002i−2i2i−2i0000
χ18222222222-2-22-2-22-2-2-22-2222222220000000000000000-2-2-2-2000000000000000000000000−2i2i−2i2i0000
χ19222222222-2-22-2-22-2-2-22-2-2-2-2-2-2-2-2-2000000000000000022220000000000000000000000002i−2i−2i2i0000
χ20222222222-2-22-2-22-2-2-22-2-2-2-2-2-2-2-2-200000000000000002222000000000000000000000000−2i2i2i−2i0000
χ2122222222-22-2-2-22-222-2-2-2000000002222-2-2-2-200000000000000002i2i−2i−2i00002i2i−2i−2i0000000000000000
χ2222222222-22-2-2-22-222-2-2-2000000002222-2-2-2-20000000000000000−2i−2i2i2i0000−2i−2i2i2i0000000000000000
χ2322222222-22-2-2-22-222-2-2-200000000-2-2-2-2222200000000000000002i2i−2i−2i0000−2i−2i2i2i0000000000000000
χ2422222222-22-2-2-22-222-2-2-200000000-2-2-2-222220000000000000000−2i−2i2i2i00002i2i−2i−2i0000000000000000
χ252222-2-2-2-22-2-22-2-2-2222-22000000002i2i−2i−2i2i2i−2i−2i00000000000022-2-200002i2i−2i−2i00000000000000000000
χ262222-2-2-2-22-2-22-2-2-2222-22000000002i2i−2i−2i2i2i−2i−2i000000000000-2-2220000−2i−2i2i2i00000000000000000000
χ272222-2-2-2-22-2-22-2-2-2222-2200000000−2i−2i2i2i−2i−2i2i2i00000000000022-2-20000−2i−2i2i2i00000000000000000000
χ282222-2-2-2-22-2-22-2-2-2222-2200000000−2i−2i2i2i−2i−2i2i2i000000000000-2-22200002i2i−2i−2i00000000000000000000
χ292222-2-2-2-2-22-2-2-222-2-22222222-2-2-2-2000000000000000022-2-200000000000000002-22-2000000000000
χ302222-2-2-2-2-22-2-2-222-2-22222222-2-2-2-2000000000000000022-2-20000000000000000-22-22000000000000
χ312222-2-2-2-2-22-2-2-222-2-2222-2-2-2-222220000000000000000-2-22200000000000000002-2-22000000000000
χ322222-2-2-2-2-22-2-2-222-2-2222-2-2-2-222220000000000000000-2-2220000000000000000-222-2000000000000
χ332222-2-2-2-2-2-22-22-2222-22-22222-2-2-2-22i2i−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i-2-22200000000000000000000000000000000
χ342222-2-2-2-2-2-22-22-2222-22-22222-2-2-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i−2i−2i2i2i2i2i-2-22200000000000000000000000000000000
χ352222-2-2-2-2-2-22-22-2222-22-2-2-2-2-222222i2i−2i−2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i22-2-200000000000000000000000000000000
χ362222-2-2-2-2-2-22-22-2222-22-2-2-2-2-22222−2i−2i2i2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i22-2-200000000000000000000000000000000
χ3722-2-222-2-222-2-22-2-22-2-22222-2-222-2-200000000000000002-22-200002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ3822-2-222-2-222-2-22-2-22-2-22222-2-222-2-200000000000000002-22-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ3922-2-222-2-222-2-22-2-22-2-222-2-222-2-2220000000000000000-22-2200002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ4022-2-222-2-222-2-22-2-22-2-222-2-222-2-2220000000000000000-22-220000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ4122-2-222-2-22-22-2-22-2-2222-222-2-222-2-20000000000000000-22-2200000000000000000000000000002i−2i2i−2i
χ4222-2-222-2-22-22-2-22-2-2222-222-2-222-2-20000000000000000-22-220000000000000000000000000000−2i2i−2i2i
χ4322-2-222-2-22-22-2-22-2-2222-2-2-222-2-22200000000000000002-22-200000000000000000000000000002i−2i−2i2i
χ4422-2-222-2-22-22-2-22-2-2222-2-2-222-2-22200000000000000002-22-20000000000000000000000000000−2i2i2i−2i
χ4522-2-222-2-2-2222-2-222-22-2-2000000000000000022-2-222-2-200002-22-22-2-22000000000000000000000000
χ4622-2-222-2-2-2222-2-222-22-2-2000000000000000022-2-222-2-20000-22-22-222-2000000000000000000000000
χ4722-2-222-2-2-2222-2-222-22-2-20000000000000000-2-222-2-22200002-22-2-222-2000000000000000000000000
χ4822-2-222-2-2-2222-2-222-22-2-20000000000000000-2-222-2-2220000-22-222-2-22000000000000000000000000
χ4922-2-2-2-2222-22-2-2222-2-2-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000002-2-222i−2i2i−2i0000000000000000
χ5022-2-2-2-2222-22-2-2222-2-2-2200000000000000002i2i−2i−2i−2i−2i2i2i000000000000-222-2−2i2i−2i2i0000000000000000
χ5122-2-2-2-2222-22-2-2222-2-2-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000002-2-22−2i2i−2i2i0000000000000000
χ5222-2-2-2-2222-22-2-2222-2-2-220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000-222-22i−2i2i−2i0000000000000000
χ5322-2-2-2-222-2222-2-2-2-22-22222-2-2-2-22200000000000000002-2-22000000000000000000002i−2i2i−2i00000000
χ5422-2-2-2-222-2222-2-2-2-22-22222-2-2-2-22200000000000000002-2-2200000000000000000000−2i2i−2i2i00000000
χ5522-2-2-2-222-2222-2-2-2-22-222-2-22222-2-20000000000000000-222-2000000000000000000002i−2i−2i2i00000000
χ5622-2-2-2-222-2222-2-2-2-22-222-2-22222-2-20000000000000000-222-200000000000000000000−2i2i2i−2i00000000
χ5722-2-2-2-222-2-2-2222-22-222-222-2-2-2-2220000000000000000-222-22-2-22000000002-2-220000000000000000
χ5822-2-2-2-222-2-2-2222-22-222-222-2-2-2-2220000000000000000-222-2-222-200000000-222-20000000000000000
χ5922-2-2-2-222-2-2-2222-22-222-2-2-22222-2-200000000000000002-2-222-2-2200000000-222-20000000000000000
χ6022-2-2-2-222-2-2-2222-22-222-2-2-22222-2-200000000000000002-2-22-222-2000000002-2-220000000000000000
χ6144444444-4-44-44-4-4-4-44-44000000000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4444444-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000
χ6344-4-444-4-4-4-4-44444-44-4-44000000000000000000000000000000000000000000000000000000000000
χ6444-4-4-4-44444-4-44-44-444-4-4000000000000000000000000000000000000000000000000000000000000
χ654-44-44i−4i4i−4i0000000000002i2−2i22i2−2i222−2222−2200002+2i−2−2i2−2i−2+2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000000000000000
χ664-44-44i−4i4i−4i0000000000002i2−2i22i2−2i222−2222−220000−2−2i2+2i−2+2i2−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000000000000000
χ674-44-44i−4i4i−4i000000000000−2i22i2−2i22i2−2222−222200002+2i−2−2i2−2i−2+2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000000000000000
χ684-44-44i−4i4i−4i000000000000−2i22i2−2i22i2−2222−22220000−2−2i2+2i−2+2i2−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000000000000000
χ694-44-4−4i4i−4i4i0000000000002i2−2i22i2−2i2−2222−222200002−2i−2+2i2+2i−2−2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000000000000000
χ704-44-4−4i4i−4i4i0000000000002i2−2i22i2−2i2−2222−22220000−2+2i2−2i−2−2i2+2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000000000000000
χ714-44-4−4i4i−4i4i000000000000−2i22i2−2i22i222−2222−2200002−2i−2+2i2+2i−2−2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000000000000000
χ724-44-4−4i4i−4i4i000000000000−2i22i2−2i22i222−2222−220000−2+2i2−2i−2−2i2+2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000000000000000
χ734-4-444i−4i−4i4i0000000000002i2−2i2−2i22i222−22−22222−2i−2+2i2+2i−2−2i00002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000000000000000
χ744-4-444i−4i−4i4i0000000000002i2−2i2−2i22i222−22−2222−2+2i2−2i−2−2i2+2i0000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000000000000000
χ754-4-444i−4i−4i4i000000000000−2i22i22i2−2i2−222222−222−2i−2+2i2+2i−2−2i0000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000000000000000
χ764-4-444i−4i−4i4i000000000000−2i22i22i2−2i2−222222−22−2+2i2−2i−2−2i2+2i00002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000000000000000
χ774-4-44−4i4i4i−4i0000000000002i2−2i2−2i22i2−222222−222+2i−2−2i2−2i−2+2i00002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000000000000000
χ784-4-44−4i4i4i−4i0000000000002i2−2i2−2i22i2−222222−22−2−2i2+2i−2+2i2−2i0000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000000000000000
χ794-4-44−4i4i4i−4i000000000000−2i22i22i2−2i222−22−22222+2i−2−2i2−2i−2+2i0000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000000000000000
χ804-4-44−4i4i4i−4i000000000000−2i22i22i2−2i222−22−2222−2−2i2+2i−2+2i2−2i00002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.