Finite Group Databasebeta

← Group #263188

Character table — Group #263188

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222224444444444444444444444444488888888888888161616161616161632323232
order12222244444444888888884444444444444488888888888822444488888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ911111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ1011111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ1111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-11-11
χ1211111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1111-11-1
χ1311111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-11
χ1411111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-111-1
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-111-111-1
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ1722222222-2-2-2-222000000002222-2-22222-2-2-2-200000000000022-2-2-2-200000000000000000000
χ1822222222-2-2-2-222000000002222-2-2-2-2-2-22222000000000000-2-2-2-22200000000000000000000
χ1922222222-2-2-2-22200000000-2-2-2-2-2-22222-2-2-2-2000000000000-2-2222200000000000000000000
χ2022222222-2-2-2-22200000000-2-2-2-2-2-2-2-2-2-222220000000000002222-2-200000000000000000000
χ21222222-2-22222-2-22222222222-2-2-2-20000000000000000-2-2-2-2002-20022-2-20000000000000000
χ22222222-2-22222-2-222222222-2-222-2-20000000000000000-2-2-2-200-2200-2-2220000000000000000
χ23222222-2-22222-2-2-2-2-2-2-2-2-2-222-2-2-2-200000000000000002222002-200-2-2220000000000000000
χ24222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222-2-20000000000000000222200-220022-2-20000000000000000
χ25222222-2-2-2-2-2-2-2-20000000022-2-222000000002i2i2i2i−2i−2i−2i−2i000000-220000002i2i−2i−2i000000000000
χ26222222-2-2-2-2-2-2-2-20000000022-2-22200000000−2i−2i−2i−2i2i2i2i2i000000-22000000−2i−2i2i2i000000000000
χ27222222-2-2-2-2-2-2-2-200000000-2-22222000000002i2i2i2i−2i−2i−2i−2i0000002-2000000−2i−2i2i2i000000000000
χ28222222-2-2-2-2-2-2-2-200000000-2-2222200000000−2i−2i−2i−2i2i2i2i2i0000002-20000002i2i−2i−2i000000000000
χ292222-2-22-2-2-2222-22222-2-2-2-200002-2000000000000000022-2-20000000000000000002-22-20000
χ302222-2-22-2-2-2222-22222-2-2-2-200002-2000000000000000022-2-2000000000000000000-22-220000
χ312222-2-22-2-2-2222-2-2-2-2-2222200002-20000000000000000-2-2220000000000000000002-2-220000
χ322222-2-22-2-2-2222-2-2-2-2-2222200002-20000000000000000-2-222000000000000000000-222-20000
χ332222-2-2-22-2-222-222222-2-2-2-20000-220000000000000000-2-222000000000000002-22-200000000
χ342222-2-2-22-2-222-222222-2-2-2-20000-220000000000000000-2-22200000000000000-22-2200000000
χ352222-2-2-22-2-222-22-2-2-2-222220000-22000000000000000022-2-2000000000000002-2-2200000000
χ362222-2-2-22-2-222-22-2-2-2-222220000-22000000000000000022-2-200000000000000-222-200000000
χ3722-2-22-2220000-2-222−2−222−2−22-22-20022-2-2000022−2−222−2−22−22−22-200002−22−22−22−2000000000000
χ3822-2-22-2220000-2-222−2−222−2−22-22-200-2-2220000−2−222−2−2222−22−2-2200002−22−2−22−22000000000000
χ3922-2-22-2220000-2-222−2−222−2−2-22-220022-2-2000022−2−222−2−22−22−2-220000−22−22−22−22000000000000
χ4022-2-22-2220000-2-222−2−222−2−2-22-2200-2-2220000−2−222−2−2222−22−22-20000−22−222−22−2000000000000
χ4122-2-22-2220000-2-2−2−222−2−2222-22-20022-2-20000−2−222−2−222−22−222-20000−22−22−22−22000000000000
χ4222-2-22-2220000-2-2−2−222−2−2222-22-200-2-222000022−2−222−2−2−22−22-220000−22−222−22−2000000000000
χ4322-2-22-2220000-2-2−2−222−2−222-22-220022-2-20000−2−222−2−222−22−22-2200002−22−22−22−2000000000000
χ4422-2-22-2220000-2-2−2−222−2−222-22-2200-2-222000022−2−222−2−2−22−222-200002−22−2−22−22000000000000
χ4522-2-22-2-2-200002222−2−222−2−22-2-220000002i2i−2i−2ii2i2−i2−i2−i2−i2i2i2−22−2200002i−2i2−2−22i2−i2−i2i2000000000000
χ4622-2-22-2-2-200002222−2−222−2−22-2-22000000−2i−2i2i2i−i2−i2i2i2i2i2−i2−i2−22−220000−2i2i2−2−22−i2i2i2−i2000000000000
χ4722-2-22-2-2-200002222−2−222−2−2-222-20000002i2i−2i−2ii2i2−i2−i2−i2−i2i2i2−22−220000−2i2i−222−2−i2i2i2−i2000000000000
χ4822-2-22-2-2-200002222−2−222−2−2-222-2000000−2i−2i2i2i−i2−i2i2i2i2i2−i2−i2−22−2200002i−2i−222−2i2−i2−i2i2000000000000
χ4922-2-22-2-2-2000022−2−222−2−2222-2-220000002i2i−2i−2i−i2−i2i2i2i2i2−i2−i22−22−200002i−2i−222−2−i2i2i2−i2000000000000
χ5022-2-22-2-2-2000022−2−222−2−2222-2-22000000−2i−2i2i2ii2i2−i2−i2−i2−i2i2i22−22−20000−2i2i−222−2i2−i2−i2i2000000000000
χ5122-2-22-2-2-2000022−2−222−2−222-222-20000002i2i−2i−2i−i2−i2i2i2i2i2−i2−i22−22−20000−2i2i2−2−22i2−i2−i2i2000000000000
χ5222-2-22-2-2-2000022−2−222−2−222-222-2000000−2i−2i2i2ii2i2−i2−i2−i2−i2i2i22−22−200002i−2i2−2−22−i2i2i2−i2000000000000
χ534444-4-44-444-4-44-4000000000000-440000000000000000000000000000000000000000000000
χ544444-4-4-4444-4-4-440000000000004-40000000000000000000000000000000000000000000000
χ5544-4-4-444-40000-442222−22−22−22−222222000000000000000000000022−22−222200000000000000000000000000
χ5644-4-4-444-40000-44−22−2222222222−22−220000000000000000000000−222222−2200000000000000000000000000
χ5744-4-4-44-4400004-42222−22−22−22−2222220000000000000000000000−222222−2200000000000000000000000000
χ5844-4-4-44-4400004-4−22−2222222222−22−22000000000000000000000022−22−222200000000000000000000000000
χ594-44-40000004-40000004-44-40000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000
χ604-44-40000004-40000004-44-4000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000
χ614-44-40000004-4000000-44-440000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000
χ624-44-40000004-4000000-44-44000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000
χ634-44-4000000-44004i−4i4i−4i00000000002i−2i2i−2i−2i2i−2i2i2-22-2-22-22000000000000000000000000000000
χ644-44-4000000-44004i−4i4i−4i0000000000−2i2i−2i2i2i−2i2i−2i-22-222-22-2000000000000000000000000000000
χ654-44-4000000-4400−4i4i−4i4i00000000002i−2i2i−2i−2i2i−2i2i-22-222-22-2000000000000000000000000000000
χ664-44-4000000-4400−4i4i−4i4i0000000000−2i2i−2i2i2i−2i2i−2i2-22-2-22-22000000000000000000000000000000
χ674-4-4400004i−4i00002i2−2i2−2i22i222−22−22220000002i−2i−2i2i2-2-222ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000000000
χ684-4-4400004i−4i00002i2−2i2−2i22i222−22−2222000000−2i2i2i−2i-222-2−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000000000
χ694-4-4400004i−4i0000−2i22i22i2−2i2−222222−220000002i−2i−2i2i2-2-22−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000000000
χ704-4-4400004i−4i0000−2i22i22i2−2i2−222222−22000000−2i2i2i−2i-222-22ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000000000
χ714-4-440000−4i4i00002i2−2i2−2i22i2−222222−220000002i−2i−2i2i-222-2−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000000000
χ724-4-440000−4i4i00002i2−2i2−2i22i2−222222−22000000−2i2i2i−2i2-2-222ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000000000
χ734-4-440000−4i4i0000−2i22i22i2−2i222−22−22220000002i−2i−2i2i-222-22ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000000000
χ744-4-440000−4i4i0000−2i22i22i2−2i222−22−2222000000−2i2i2i−2i2-2-22−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000000000

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