Finite Group Databasebeta

← Group #450227

Character table — Group #450227

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222888888888888888888888888888888888888161616161616161616161616
order12224444222222444444222244444444888888888888888888888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ31111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1-1-1-1-1
χ51111111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ61111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-1
χ71111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111
χ81111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-111
χ911111111111111111111-1-111-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ1011111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111
χ1111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ1211111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-11111
χ172222-2-2-2-22-2-22-2-222-2-2220000000022-2-22i2i−2i−2i00002i2i−2i−2i000000000000000000000000
χ182222-2-2-2-22-2-22-2-222-2-2220000000022-2-2−2i−2i2i2i0000−2i−2i2i2i000000000000000000000000
χ192222-2-2-2-22-2-22-2-222-2-22200000000-2-2222i2i−2i−2i0000−2i−2i2i2i000000000000000000000000
χ202222-2-2-2-22-2-22-2-222-2-22200000000-2-222−2i−2i2i2i00002i2i−2i−2i000000000000000000000000
χ212222-2-2-2-2-22-2-22-22-2222-2002200-2-2000000002i2i−2i−2i000000002i2i−2i−2i0000000000000000
χ222222-2-2-2-2-22-2-22-22-2222-2002200-2-200000000−2i−2i2i2i00000000−2i−2i2i2i0000000000000000
χ232222-2-2-2-2-22-2-22-22-2222-200-2-20022000000002i2i−2i−2i00000000−2i−2i2i2i0000000000000000
χ242222-2-2-2-2-22-2-22-22-2222-200-2-2002200000000−2i−2i2i2i000000002i2i−2i−2i0000000000000000
χ252222-2-2-2-2-2-22-2-22-2222-222200-2-20000000000000000002i2i−2i−2i00002i2i−2i−2i000000000000
χ262222-2-2-2-2-2-22-2-22-2222-222200-2-2000000000000000000−2i−2i2i2i0000−2i−2i2i2i000000000000
χ272222-2-2-2-2-2-22-2-22-2222-22-2-200220000000000000000002i2i−2i−2i0000−2i−2i2i2i000000000000
χ282222-2-2-2-2-2-22-2-22-2222-22-2-20022000000000000000000−2i−2i2i2i00002i2i−2i−2i000000000000
χ292-2-2222-2-2222-2-2-2222-2-2-22-22-22-22-2000000000000000000000000000000002-2000000
χ302-2-2222-2-2222-2-2-2222-2-2-22-2-222-2-2200000000000000000000000000000000-22000000
χ312-2-2222-2-2222-2-2-2222-2-2-2-222-2-222-200000000000000000000000000000000-22000000
χ322-2-2222-2-2222-2-2-2222-2-2-2-22-22-22-22000000000000000000000000000000002-2000000
χ332-2-2222-2-2-22-22-22-22-222-200000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000002-200
χ342-2-2222-2-2-22-22-22-22-222-200000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000-2200
χ352-2-2222-2-2-22-22-22-22-222-20000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000-2200
χ362-2-2222-2-2-22-22-22-22-222-20000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000002-200
χ372-2-2222-2-2-2-2222-22-2-22-220000000000002i−2i2i−2i000000002i−2i2i−2i0000000000000000002-2
χ382-2-2222-2-2-2-2222-22-2-22-220000000000002i−2i2i−2i00000000−2i2i−2i2i000000000000000000-22
χ392-2-2222-2-2-2-2222-22-2-22-22000000000000−2i2i−2i2i000000002i−2i2i−2i000000000000000000-22
χ402-2-2222-2-2-2-2222-22-2-22-22000000000000−2i2i−2i2i00000000−2i2i−2i2i0000000000000000002-2
χ412-2-22-2-222222-2-2-2-2-2-222200000000000000002-2-2200002-2-22000000000000002-20000
χ422-2-22-2-222222-2-2-2-2-2-222200000000000000002-2-220000-222-200000000000000-220000
χ432-2-22-2-222222-2-2-2-2-2-22220000000000000000-222-200002-2-2200000000000000-220000
χ442-2-22-2-222222-2-2-2-2-2-22220000000000000000-222-20000-222-2000000000000002-20000
χ452-2-22-2-222-22-22-222-22-2-22002-200-2200002-2-22000000000000000000002-20000000000
χ462-2-22-2-222-22-22-222-22-2-22002-200-220000-222-200000000000000000000-220000000000
χ472-2-22-2-222-22-22-222-22-2-2200-22002-200002-2-2200000000000000000000-220000000000
χ482-2-22-2-222-22-22-222-22-2-2200-22002-20000-222-2000000000000000000002-20000000000
χ492-2-22-2-222-2-2222-2-222-22-22-200-22000000000000002-2-22000000000000002-200000000
χ502-2-22-2-222-2-2222-2-222-22-22-200-2200000000000000-222-200000000000000-2200000000
χ512-2-22-2-222-2-2222-2-222-22-2-22002-2000000000000002-2-2200000000000000-2200000000
χ522-2-22-2-222-2-2222-2-222-22-2-22002-200000000000000-222-2000000000000002-200000000
χ53444444444-4-44-4-4-4-444-4-4000000000000000000000000000000000000000000000000
χ5444444444-44-4-44-4-44-4-4-44000000000000000000000000000000000000000000000000
χ5544444444-4-44-4-444-4-4-44-4000000000000000000000000000000000000000000000000
χ564444-4-4-4-4444444-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ5744-4-44i−4i4i−4i000000000000000000002-22i−2i00000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000
χ5844-4-44i−4i4i−4i000000000000000000002-22i−2i0000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000
χ5944-4-44i−4i4i−4i00000000000000000000-22−2i2i00000000000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3000000000000
χ6044-4-44i−4i4i−4i00000000000000000000-22−2i2i0000000000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3000000000000
χ6144-4-4−4i4i−4i4i000000000000000000002-2−2i2i00000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000
χ6244-4-4−4i4i−4i4i000000000000000000002-2−2i2i0000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000
χ6344-4-4−4i4i−4i4i00000000000000000000-222i−2i00000000000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ000000000000
χ6444-4-4−4i4i−4i4i00000000000000000000-222i−2i0000000000000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ000000000000
χ654-4-4444-4-44-4-4-444-4-44-444000000000000000000000000000000000000000000000000
χ664-4-44-4-4444-4-4-44444-44-4-4000000000000000000000000000000000000000000000000
χ678-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000
χ688-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000

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