Finite Group Databasebeta

← Group #263185

Character table — Group #263185

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222224444444444444444444444444488888888888888161616161616161632323232
order12222244444444888888884444444444444488888888888822444488888888224444448888
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
χ5111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-111-1-1
χ6111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111-1111-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-11-1-1-111111-1-1
χ911111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-11-1-111-11-11-1
χ1011111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-111-1-11-11-11
χ1111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-111111-11-1-111-1-11-11
χ1211111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-11-111-1-111-11-1
χ1311111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-111-1-11
χ1411111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111-1-111-1
χ1511111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-1-1-1111-1-1-1-11-111-1
χ1611111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-11111-11-1-11
χ1722222222-2-2-2-22222222222-2-222-2-20000000000000000-2-2-2-2002-20022-2-20000000000000000
χ1822222222-2-2-2-22222222222-2-2-2-2220000000000000000-2-2-2-200-2200-2-2220000000000000000
χ1922222222-2-2-2-222-2-2-2-2-2-2-2-2-2-222-2-200000000000000002222002-200-2-2220000000000000000
χ2022222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2220000000000000000222200-220022-2-20000000000000000
χ21222222-2-22222-2-200000000-2-222222222-2-2-2-200000000000022-2-2-2-200000000000000000000
χ22222222-2-22222-2-200000000-2-22222-2-2-2-22222000000000000-2-2-2-22200000000000000000000
χ23222222-2-22222-2-200000000-2-2-2-2-2-22222-2-2-2-2000000000000-2-2222200000000000000000000
χ24222222-2-22222-2-200000000-2-2-2-2-2-2-2-2-2-222220000000000002222-2-200000000000000000000
χ25222222-2-2-2-2-2-2-2-2000000002222-2-2000000002i2i2i2i−2i−2i−2i−2i000000-220000002i2i−2i−2i000000000000
χ26222222-2-2-2-2-2-2-2-2000000002222-2-200000000−2i−2i−2i−2i2i2i2i2i000000-22000000−2i−2i2i2i000000000000
χ27222222-2-2-2-2-2-2-2-20000000022-2-222000000002i2i2i2i−2i−2i−2i−2i0000002-2000000−2i−2i2i2i000000000000
χ28222222-2-2-2-2-2-2-2-20000000022-2-22200000000−2i−2i−2i−2i2i2i2i2i0000002-20000002i2i−2i−2i000000000000
χ292222-2-2-2-222-2-2222222-2-2-2-22-20000000000000000000022-2-200000000000000020002-2-20000
χ302222-2-2-2-222-2-2222222-2-2-2-22-20000000000000000000022-2-2000000000000000-2000-2220000
χ312222-2-2-2-222-2-222-2-2-2-222222-200000000000000000000-2-2220000000000000002000-22-20000
χ322222-2-2-2-222-2-222-2-2-2-222222-200000000000000000000-2-222000000000000000-20002-220000
χ332222-2-2-2-2-2-222222222-2-2-2-2-2200000000000000000000-2-2220000000000000020-22-20000000
χ342222-2-2-2-2-2-222222222-2-2-2-2-2200000000000000000000-2-22200000000000000-202-220000000
χ352222-2-2-2-2-2-22222-2-2-2-22222-220000000000000000000022-2-20000000000000020-2-220000000
χ362222-2-2-2-2-2-22222-2-2-2-22222-220000000000000000000022-2-200000000000000-2022-20000000
χ3722-2-22-2002-22-200i2i2−i2−i2i2i2−i2−i2002i−2i2i−2i000022-2-2i2i2−i2−i2i2i2−i2−i2i2−i2i2−i200002i−2i2−22−22−22−2000000000000
χ3822-2-22-2002-22-200i2i2−i2−i2i2i2−i2−i2002i−2i2i−2i0000-2-222−i2−i2i2i2−i2−i2i2i2i2−i2i2−i20000−2i2i2−22−2−22−22000000000000
χ3922-2-22-2002-22-200i2i2−i2−i2i2i2−i2−i200−2i2i−2i2i000022-2-2i2i2−i2−i2i2i2−i2−i2i2−i2i2−i20000−2i2i−22−22−22−22000000000000
χ4022-2-22-2002-22-200i2i2−i2−i2i2i2−i2−i200−2i2i−2i2i0000-2-222−i2−i2i2i2−i2−i2i2i2i2−i2i2−i200002i−2i−22−222−22−2000000000000
χ4122-2-22-2002-22-200−i2−i2i2i2−i2−i2i2i2002i−2i2i−2i000022-2-2−i2−i2i2i2−i2−i2i2i2−i2i2−i2i200002i−2i−22−22−22−22000000000000
χ4222-2-22-2002-22-200−i2−i2i2i2−i2−i2i2i2002i−2i2i−2i0000-2-222i2i2−i2−i2i2i2−i2−i2−i2i2−i2i20000−2i2i−22−222−22−2000000000000
χ4322-2-22-2002-22-200−i2−i2i2i2−i2−i2i2i200−2i2i−2i2i000022-2-2−i2−i2i2i2−i2−i2i2i2−i2i2−i2i20000−2i2i2−22−22−22−2000000000000
χ4422-2-22-2002-22-200−i2−i2i2i2−i2−i2i2i200−2i2i−2i2i0000-2-222i2i2−i2−i2i2i2−i2−i2−i2i2−i2i200002i−2i2−22−2−22−22000000000000
χ4522-2-22-200-22-2200i2i2−i2−i2i2i2−i2−i2002i−2i−2i2i2i2i−2i−2i000022−2−2−2−222−i2i2−i2i22-200002−2−22−i2i2i2−i2000000000000
χ4622-2-22-200-22-2200i2i2−i2−i2i2i2−i2−i2002i−2i−2i2i−2i−2i2i2i0000−2−22222−2−2−i2i2−i2i2-2200002−2−22i2−i2−i2i2000000000000
χ4722-2-22-200-22-2200i2i2−i2−i2i2i2−i2−i200−2i2i2i−2i2i2i−2i−2i000022−2−2−2−222−i2i2−i2i2-220000−222−2i2−i2−i2i2000000000000
χ4822-2-22-200-22-2200i2i2−i2−i2i2i2−i2−i200−2i2i2i−2i−2i−2i2i2i0000−2−22222−2−2−i2i2−i2i22-20000−222−2−i2i2i2−i2000000000000
χ4922-2-22-200-22-2200−i2−i2i2i2−i2−i2i2i2002i−2i−2i2i2i2i−2i−2i0000−2−22222−2−2i2−i2i2−i22-20000−222−2i2−i2−i2i2000000000000
χ5022-2-22-200-22-2200−i2−i2i2i2−i2−i2i2i2002i−2i−2i2i−2i−2i2i2i000022−2−2−2−222i2−i2i2−i2-220000−222−2−i2i2i2−i2000000000000
χ5122-2-22-200-22-2200−i2−i2i2i2−i2−i2i2i200−2i2i2i−2i2i2i−2i−2i0000−2−22222−2−2i2−i2i2−i2-2200002−2−22−i2i2i2−i2000000000000
χ5222-2-22-200-22-2200−i2−i2i2i2−i2−i2i2i200−2i2i2i−2i−2i−2i2i2i000022−2−2−2−222i2−i2i2−i22-200002−2−22i2−i2−i2i2000000000000
χ534444-4-44444-4-4-4-400000000-4400000000000000000000000000000000000000000000000000
χ544444-4-444-4-444-4-4000000004-400000000000000000000000000000000000000000000000000
χ5544-4-4-44004-4-44002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ5644-4-4-44004-4-4400−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ5744-4-4-4400-444-4002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ5844-4-4-4400-444-400−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ594-44-4000000004-400004-44-40000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000
χ604-44-4000000004-400004-44-4000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000
χ614-44-4000000004-40000-44-440000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000
χ624-44-4000000004-40000-44-44000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000
χ634-44-400000000-444i−4i4i−4i00000000002i−2i2i−2i−2i2i−2i2i2-22-2-22-22000000000000000000000000000000
χ644-44-400000000-444i−4i4i−4i0000000000−2i2i−2i2i2i−2i2i−2i-22-222-22-2000000000000000000000000000000
χ654-44-400000000-44−4i4i−4i4i00000000002i−2i2i−2i−2i2i−2i2i-22-222-22-2000000000000000000000000000000
χ664-44-400000000-44−4i4i−4i4i0000000000−2i2i−2i2i2i−2i2i−2i2-22-2-22-22000000000000000000000000000000
χ674-4-44004i−4i00000022−22−22222i2−2i2−2i22i20000002-2-22−2i2i2i−2i−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000000000000000000000
χ684-4-44004i−4i00000022−22−22222i2−2i2−2i22i2000000-222-22i−2i−2i2i2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000000000
χ694-4-44004i−4i000000−222222−22−2i22i22i2−2i20000002-2-22−2i2i2i−2i2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000000000
χ704-4-44004i−4i000000−222222−22−2i22i22i2−2i2000000-222-22i−2i−2i2i−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000000000000000000000
χ714-4-4400−4i4i00000022−22−2222−2i22i22i2−2i20000002-2-222i−2i−2i2i2ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000000000
χ724-4-4400−4i4i00000022−22−2222−2i22i22i2−2i2000000-222-2−2i2i2i−2i−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000000000
χ734-4-4400−4i4i000000−222222−222i2−2i2−2i22i20000002-2-222i−2i−2i2i−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000000000
χ744-4-4400−4i4i000000−222222−222i2−2i2−2i22i2000000-222-2−2i2i2i−2i2ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000000000

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