Finite Group Databasebeta

← Group #140213

Character table — Group #140213

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order1244888822244444448888888888448816161616161616161616161616161616888888881616161616161616244488881616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ91111-1-1-1-111111-1-1-1-11-1-1-1-11111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i
χ101111-1-1-1-111111-1-1-1-11-1-1-1-11111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−iii−i−iii
χ111111-1-1-1-111111-1-1-1-11-1-1-1-11111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1-1-111−i−iiiii−i−i
χ121111-1-1-1-111111-1-1-1-11-1-1-1-11111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-11111-1-1ii−i−i−i−iii
χ131111-1-1-1-111111-1-1-1-11-1-1-1-11111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-1-1-111ii−i−i−i−iii
χ141111-1-1-1-111111-1-1-1-11-1-1-1-11111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-11111-1-1−i−iiiii−i−i
χ151111-1-1-1-111111-1-1-1-11-1-1-1-11111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−iii
χ161111-1-1-1-111111-1-1-1-11-1-1-1-11111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ii−i−iii−i−i
χ172222222222222-2-2-2-222222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ182222222222222-2-2-2-222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ1922222222-22-2-222222-2-2-2222222-2-2-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ2022222222-22-2-222222-2-2-2222222-2-2-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ2122222222-22-2-22-2-2-2-2-2-2-222-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2222222222-22-2-22-2-2-2-2-2-2-222-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ232222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ242222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ252222-2-2-2-2-22-2-222222-222-2-2-2-2-2-222-2-2220000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ262222-2-2-2-2-22-2-222222-222-2-2-2-2-2-222-2-222000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ272222-2-2-2-2-22-2-22-2-2-2-2-222-2-222222222-2-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ282222-2-2-2-2-22-2-22-2-2-2-2-222-2-222222222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2922-2-22i2i−2i−2i222-2-20000-22i−2i2i−2i00002i−2i00002ζ22ζ2−2ζ2−2ζ22ζ62ζ6−2ζ6−2ζ6000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i2−22−2i2−i2i2−i20000000000000000
χ3022-2-22i2i−2i−2i222-2-20000-22i−2i2i−2i00002i−2i00002ζ22ζ2−2ζ2−2ζ22ζ62ζ6−2ζ6−2ζ600000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−22−22−i2i2−i2i20000000000000000
χ3122-2-22i2i−2i−2i222-2-20000-22i−2i2i−2i00002i−2i0000−2ζ2−2ζ22ζ22ζ2−2ζ6−2ζ62ζ62ζ6000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−22−22−i2i2−i2i20000000000000000
χ3222-2-22i2i−2i−2i222-2-20000-22i−2i2i−2i00002i−2i0000−2ζ2−2ζ22ζ22ζ2−2ζ6−2ζ62ζ62ζ600000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2−22−2i2−i2i2−i20000000000000000
χ3322-2-22i2i−2i−2i2-2-2-222i2i−2i−2i2−2i2i−2i2i22-2-22i−2i2i−2i2-2000000000000000000000000000000002-2002i−2i0000000000
χ3422-2-22i2i−2i−2i2-2-2-222i2i−2i−2i2−2i2i−2i2i22-2-22i−2i2i−2i2-200000000000000000000000000000000-2200−2i2i0000000000
χ3522-2-22i2i−2i−2i2-2-2-22−2i−2i2i2i2−2i2i−2i2i-2-2222i−2i−2i2i-22000000000000000000000000000000000000000000002ζ2−2ζ22ζ6−2ζ6
χ3622-2-22i2i−2i−2i2-2-2-22−2i−2i2i2i2−2i2i−2i2i-2-2222i−2i−2i2i-2200000000000000000000000000000000000000000000−2ζ22ζ2−2ζ62ζ6
χ3722-2-22i2i−2i−2i-22-22-200002−2i2i2i−2i0000−2i2i0000000000002ζ62ζ6−2ζ6−2ζ62ζ22ζ2−2ζ2−2ζ21+i−1−i−1−i1+i1−i−1+i−1+i1−ii2−i2−i2i2−222−20000000000000000
χ3822-2-22i2i−2i−2i-22-22-200002−2i2i2i−2i0000−2i2i0000000000002ζ62ζ6−2ζ6−2ζ62ζ22ζ2−2ζ2−2ζ2−1−i1+i1+i−1−i−1+i1−i1−i−1+i−i2i2i2−i22−2−220000000000000000
χ3922-2-22i2i−2i−2i-22-22-200002−2i2i2i−2i0000−2i2i000000000000−2ζ6−2ζ62ζ62ζ6−2ζ2−2ζ22ζ22ζ21+i−1−i−1−i1+i1−i−1+i−1+i1−i−i2i2i2−i22−2−220000000000000000
χ4022-2-22i2i−2i−2i-22-22-200002−2i2i2i−2i0000−2i2i000000000000−2ζ6−2ζ62ζ62ζ6−2ζ2−2ζ22ζ22ζ2−1−i1+i1+i−1−i−1+i1−i1−i−1+ii2−i2−i2i2−222−20000000000000000
χ4122-2-22i2i−2i−2i-2-22222i2i−2i−2i-22i−2i−2i2i22-2-2−2i2i−2i2i-2200000000000000000000000000000000000000002ζ2−2ζ22ζ6−2ζ60000
χ4222-2-22i2i−2i−2i-2-22222i2i−2i−2i-22i−2i−2i2i22-2-2−2i2i−2i2i-220000000000000000000000000000000000000000−2ζ22ζ2−2ζ62ζ60000
χ4322-2-22i2i−2i−2i-2-2222−2i−2i2i2i-22i−2i−2i2i-2-222−2i2i2i−2i2-200000000000000000000000000000000002-2002i−2i00000000
χ4422-2-22i2i−2i−2i-2-2222−2i−2i2i2i-22i−2i−2i2i-2-222−2i2i2i−2i2-20000000000000000000000000000000000-2200−2i2i00000000
χ4522-2-2−2i−2i2i2i222-2-20000-2−2i2i−2i2i0000−2i2i00002ζ62ζ6−2ζ6−2ζ62ζ22ζ2−2ζ2−2ζ2000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−22−22i2−i2i2−i20000000000000000
χ4622-2-2−2i−2i2i2i222-2-20000-2−2i2i−2i2i0000−2i2i00002ζ62ζ6−2ζ6−2ζ62ζ22ζ2−2ζ2−2ζ200000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2−22−2−i2i2−i2i20000000000000000
χ4722-2-2−2i−2i2i2i222-2-20000-2−2i2i−2i2i0000−2i2i0000−2ζ6−2ζ62ζ62ζ6−2ζ2−2ζ22ζ22ζ2000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i2−22−2−i2i2−i2i20000000000000000
χ4822-2-2−2i−2i2i2i222-2-20000-2−2i2i−2i2i0000−2i2i0000−2ζ6−2ζ62ζ62ζ6−2ζ2−2ζ22ζ22ζ200000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−22−22i2−i2i2−i20000000000000000
χ4922-2-2−2i−2i2i2i2-2-2-222i2i−2i−2i22i−2i2i−2i-2-222−2i2i2i−2i-22000000000000000000000000000000000000000000002ζ6−2ζ62ζ2−2ζ2
χ5022-2-2−2i−2i2i2i2-2-2-222i2i−2i−2i22i−2i2i−2i-2-222−2i2i2i−2i-2200000000000000000000000000000000000000000000−2ζ62ζ6−2ζ22ζ2
χ5122-2-2−2i−2i2i2i2-2-2-22−2i−2i2i2i22i−2i2i−2i22-2-2−2i2i−2i2i2-2000000000000000000000000000000002-200−2i2i0000000000
χ5222-2-2−2i−2i2i2i2-2-2-22−2i−2i2i2i22i−2i2i−2i22-2-2−2i2i−2i2i2-200000000000000000000000000000000-22002i−2i0000000000
χ5322-2-2−2i−2i2i2i-22-22-2000022i−2i−2i2i00002i−2i0000000000002ζ22ζ2−2ζ2−2ζ22ζ62ζ6−2ζ6−2ζ61−i−1+i−1+i1−i1+i−1−i−1−i1+ii2−i2−i2i22−2−220000000000000000
χ5422-2-2−2i−2i2i2i-22-22-2000022i−2i−2i2i00002i−2i0000000000002ζ22ζ2−2ζ2−2ζ22ζ62ζ6−2ζ6−2ζ6−1+i1−i1−i−1+i−1−i1+i1+i−1−i−i2i2i2−i2−222−20000000000000000
χ5522-2-2−2i−2i2i2i-22-22-2000022i−2i−2i2i00002i−2i000000000000−2ζ2−2ζ22ζ22ζ2−2ζ6−2ζ62ζ62ζ61−i−1+i−1+i1−i1+i−1−i−1−i1+i−i2i2i2−i2−222−20000000000000000
χ5622-2-2−2i−2i2i2i-22-22-2000022i−2i−2i2i00002i−2i000000000000−2ζ2−2ζ22ζ22ζ2−2ζ6−2ζ62ζ62ζ6−1+i1−i1−i−1+i−1−i1+i1+i−1−ii2−i2−i2i22−2−220000000000000000
χ5722-2-2−2i−2i2i2i-2-22222i2i−2i−2i-2−2i2i2i−2i-2-2222i−2i−2i2i2-200000000000000000000000000000000002-200−2i2i00000000
χ5822-2-2−2i−2i2i2i-2-22222i2i−2i−2i-2−2i2i2i−2i-2-2222i−2i−2i2i2-20000000000000000000000000000000000-22002i−2i00000000
χ5922-2-2−2i−2i2i2i-2-2222−2i−2i2i2i-2−2i2i2i−2i22-2-22i−2i2i−2i-2200000000000000000000000000000000000000002ζ6−2ζ62ζ2−2ζ20000
χ6022-2-2−2i−2i2i2i-2-2222−2i−2i2i2i-2−2i2i2i−2i22-2-22i−2i2i−2i-220000000000000000000000000000000000000000−2ζ62ζ6−2ζ22ζ20000
χ61444444444-4-44-40000-4-4-4-4-40000440000000000000000000000000000000000000000000000000000
χ6244444444-4-44-4-40000444-4-40000-4-40000000000000000000000000000000000000000000000000000
χ634444-4-4-4-44-4-44-40000-444440000-4-40000000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-4-44-4-400004-4-4440000440000000000000000000000000000000000000000000000000000
χ654-44i−4i4ζ2−4ζ24ζ6−4ζ6000002+2i−2−2i2−2i−2+2i0000022−222i2−2i20000002ζ−2ζ2ζ5−2ζ52ζ3−2ζ32ζ7−2ζ72ζ3−2ζ32ζ7−2ζ72ζ−2ζ2ζ5−2ζ500000000000000000000000000000000
χ664-44i−4i4ζ2−4ζ24ζ6−4ζ6000002+2i−2−2i2−2i−2+2i0000022−222i2−2i2000000−2ζ2ζ−2ζ52ζ5−2ζ32ζ3−2ζ72ζ7−2ζ32ζ3−2ζ72ζ7−2ζ2ζ−2ζ52ζ500000000000000000000000000000000
χ674-44i−4i4ζ2−4ζ24ζ6−4ζ600000−2−2i2+2i−2+2i2−2i00000−2222−2i22i20000002ζ−2ζ2ζ5−2ζ52ζ3−2ζ32ζ7−2ζ7−2ζ32ζ3−2ζ72ζ7−2ζ2ζ−2ζ52ζ500000000000000000000000000000000
χ684-44i−4i4ζ2−4ζ24ζ6−4ζ600000−2−2i2+2i−2+2i2−2i00000−2222−2i22i2000000−2ζ2ζ−2ζ52ζ5−2ζ32ζ3−2ζ72ζ72ζ3−2ζ32ζ7−2ζ72ζ−2ζ2ζ5−2ζ500000000000000000000000000000000
χ694-44i−4i−4ζ24ζ2−4ζ64ζ6000002+2i−2−2i2−2i−2+2i00000−2222−2i22i20000002ζ5−2ζ5−2ζ2ζ−2ζ72ζ72ζ3−2ζ3−2ζ72ζ72ζ3−2ζ32ζ5−2ζ5−2ζ2ζ00000000000000000000000000000000
χ704-44i−4i−4ζ24ζ2−4ζ64ζ6000002+2i−2−2i2−2i−2+2i00000−2222−2i22i2000000−2ζ52ζ52ζ−2ζ2ζ7−2ζ7−2ζ32ζ32ζ7−2ζ7−2ζ32ζ3−2ζ52ζ52ζ−2ζ00000000000000000000000000000000
χ714-44i−4i−4ζ24ζ2−4ζ64ζ600000−2−2i2+2i−2+2i2−2i0000022−222i2−2i20000002ζ5−2ζ5−2ζ2ζ−2ζ72ζ72ζ3−2ζ32ζ7−2ζ7−2ζ32ζ3−2ζ52ζ52ζ−2ζ00000000000000000000000000000000
χ724-44i−4i−4ζ24ζ2−4ζ64ζ600000−2−2i2+2i−2+2i2−2i0000022−222i2−2i2000000−2ζ52ζ52ζ−2ζ2ζ7−2ζ7−2ζ32ζ3−2ζ72ζ72ζ3−2ζ32ζ5−2ζ5−2ζ2ζ00000000000000000000000000000000
χ734-4−4i4i4ζ6−4ζ64ζ2−4ζ2000002−2i−2+2i2+2i−2−2i00000−22222i2−2i20000002ζ3−2ζ3−2ζ72ζ7−2ζ2ζ2ζ5−2ζ5−2ζ2ζ2ζ5−2ζ52ζ3−2ζ3−2ζ72ζ700000000000000000000000000000000
χ744-4−4i4i4ζ6−4ζ64ζ2−4ζ2000002−2i−2+2i2+2i−2−2i00000−22222i2−2i2000000−2ζ32ζ32ζ7−2ζ72ζ−2ζ−2ζ52ζ52ζ−2ζ−2ζ52ζ5−2ζ32ζ32ζ7−2ζ700000000000000000000000000000000
χ754-4−4i4i4ζ6−4ζ64ζ2−4ζ200000−2+2i2−2i−2−2i2+2i0000022−22−2i22i20000002ζ3−2ζ3−2ζ72ζ7−2ζ2ζ2ζ5−2ζ52ζ−2ζ−2ζ52ζ5−2ζ32ζ32ζ7−2ζ700000000000000000000000000000000
χ764-4−4i4i4ζ6−4ζ64ζ2−4ζ200000−2+2i2−2i−2−2i2+2i0000022−22−2i22i2000000−2ζ32ζ32ζ7−2ζ72ζ−2ζ−2ζ52ζ5−2ζ2ζ2ζ5−2ζ52ζ3−2ζ3−2ζ72ζ700000000000000000000000000000000
χ774-4−4i4i−4ζ64ζ6−4ζ24ζ2000002−2i−2+2i2+2i−2−2i0000022−22−2i22i20000002ζ7−2ζ72ζ3−2ζ32ζ5−2ζ52ζ−2ζ2ζ5−2ζ52ζ−2ζ2ζ7−2ζ72ζ3−2ζ300000000000000000000000000000000
χ784-4−4i4i−4ζ64ζ6−4ζ24ζ2000002−2i−2+2i2+2i−2−2i0000022−22−2i22i2000000−2ζ72ζ7−2ζ32ζ3−2ζ52ζ5−2ζ2ζ−2ζ52ζ5−2ζ2ζ−2ζ72ζ7−2ζ32ζ300000000000000000000000000000000
χ794-4−4i4i−4ζ64ζ6−4ζ24ζ200000−2+2i2−2i−2−2i2+2i00000−22222i2−2i20000002ζ7−2ζ72ζ3−2ζ32ζ5−2ζ52ζ−2ζ−2ζ52ζ5−2ζ2ζ−2ζ72ζ7−2ζ32ζ300000000000000000000000000000000
χ804-4−4i4i−4ζ64ζ6−4ζ24ζ200000−2+2i2−2i−2−2i2+2i00000−22222i2−2i2000000−2ζ72ζ7−2ζ32ζ3−2ζ52ζ5−2ζ2ζ2ζ5−2ζ52ζ−2ζ2ζ7−2ζ72ζ3−2ζ300000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.