Finite Group Databasebeta

← Group #228255

Character table — Group #228255

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12224444224444444444444422444444448888888888888888888822444444448888888888224488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-11-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11-11-111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-11111-1-1-1-1-1-1-1-1-1-1-11-11-1-1111111
χ5111111111111111111111111-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-1-11111111111-11-11-1-111-1-1-1-1
χ6111111111111111111111111-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-11-111-1-11111
χ7111111111111111111111111-1-11-1-111111-1-1-1-11111111111111111-1111-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-11-1-111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11-11-1-1-111-1-111
χ1011111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1-1111111-1-1-1-1-11-1111-1-111-1-1
χ1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ1211111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11-1-1-1-1-1-1-111111111-1-1-1-11111-1-111
χ1311111111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1111-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ1411111111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111
χ1511111111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-111111-1-1-1-1-1-11111-11-1111-1-1-1-111
χ1611111111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111-11-1-1-11111-1-1
χ171111-1-1-1-1-1-11iiii−i−i−i−i11-1-1111-1-1-1ii−i−i1ii−i−iiiii−i−i−i−i1111-1-1-1-1-111-11-1ii−i−ii−ii−ii−i11-1-111-1-1i−ii−i1-1i−i
χ181111-1-1-1-1-1-11iiii−i−i−i−i11-1-1111-1-1-1ii−i−i1ii−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1111ii−i−ii−i−ii−ii11-1-1-1-111−ii−ii-11−ii
χ191111-1-1-1-1-1-11iiii−i−i−i−i11-1-1111-1-1-1ii−i−i1−i−iii−i−i−i−iiiii-1-1-1-11111-111-11-1ii−i−i−iii−ii−i-1-1111-1-11i−i−ii-11−ii
χ201111-1-1-1-1-1-11iiii−i−i−i−i11-1-1111-1-1-1ii−i−i1−i−iii−i−i−i−iiiii-1-1-1-11111-1-1-1111ii−i−i−ii−ii−ii-1-111-111-1−iii−i1-1i−i
χ211111-1-1-1-1-1-11iiii−i−i−i−i11-1-11-1-1-111ii−i−i1ii−i−i−i−i−i−iiiii-1-1-1-11111111-1-1-1−i−iiii−ii−ii−i11-1-1-111-1−iii−i-11−ii
χ221111-1-1-1-1-1-11iiii−i−i−i−i11-1-11-1-1-111ii−i−i1ii−i−i−i−i−i−iiiii-1-1-1-111111-1-11-11−i−iiii−i−ii−ii11-1-11-1-11i−i−ii1-1i−i
χ231111-1-1-1-1-1-11iiii−i−i−i−i11-1-11-1-1-111ii−i−i1−i−iiiiiii−i−i−i−i1111-1-1-1-1111-1-1-1−i−iii−iii−ii−i-1-111-1-111−ii−ii1-1i−i
χ241111-1-1-1-1-1-11iiii−i−i−i−i11-1-11-1-1-111ii−i−i1−i−iiiiiii−i−i−i−i1111-1-1-1-11-1-11-11−i−iii−ii−ii−ii-1-11111-1-1i−ii−i-11−ii
χ251111-1-1-1-1-1-11−i−i−i−iiiii11-1-1111-1-1-1−i−iii1ii−i−iiiii−i−i−i−i-1-1-1-11111-111-11-1−i−iiii−i−ii−ii-1-1111-1-11−iii−i-11i−i
χ261111-1-1-1-1-1-11−i−i−i−iiiii11-1-1111-1-1-1−i−iii1ii−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1111−i−iiii−ii−ii−i-1-111-111-1i−i−ii1-1−ii
χ271111-1-1-1-1-1-11−i−i−i−iiiii11-1-1111-1-1-1−i−iii1−i−iii−i−i−i−iiiii1111-1-1-1-1-111-11-1−i−iii−ii−ii−ii11-1-111-1-1−ii−ii1-1−ii
χ281111-1-1-1-1-1-11−i−i−i−iiiii11-1-1111-1-1-1−i−iii1−i−iii−i−i−i−iiiii1111-1-1-1-1-1-1-1111−i−iii−iii−ii−i11-1-1-1-111i−ii−i-11i−i
χ291111-1-1-1-1-1-11−i−i−i−iiiii11-1-11-1-1-111−i−iii1ii−i−i−i−i−i−iiiii1111-1-1-1-1111-1-1-1ii−i−ii−i−ii−ii-1-111-1-111i−ii−i1-1−ii
χ301111-1-1-1-1-1-11−i−i−i−iiiii11-1-11-1-1-111−i−iii1ii−i−i−i−i−i−iiiii1111-1-1-1-11-1-11-11ii−i−ii−ii−ii−i-1-11111-1-1−ii−ii-11i−i
χ311111-1-1-1-1-1-11−i−i−i−iiiii11-1-11-1-1-111−i−iii1−i−iiiiiii−i−i−i−i-1-1-1-11111111-1-1-1ii−i−i−ii−ii−ii11-1-1-111-1i−i−ii-11i−i
χ321111-1-1-1-1-1-11−i−i−i−iiiii11-1-11-1-1-111−i−iii1−i−iiiiiii−i−i−i−i-1-1-1-111111-1-11-11ii−i−i−iii−ii−i11-1-11-1-11−iii−i1-1−ii
χ332222222222222222222-2-2-2-2200-200-2-2-2-2-20000000000000000000002-2-202000000-2-2220000000000000000
χ342222222222222222222-2-2-2-2200-200-2-2-2-2-2000000000000000000000-2220-200000022-2-20000000000000000
χ3522222222222-2-2-2-2-2-2-2-2-2-2-2-2200-2002222-20000000000000000000002-2-20200000022-2-20000000000000000
χ3622222222222-2-2-2-2-2-2-2-2-2-2-2-2200-2002222-2000000000000000000000-2220-2000000-2-2220000000000000000
χ3722222222-2-2-2000000002222-222-2220000-2222222-2-222-2-200000000-2000-200000-2-200000000000000000000
χ3822222222-2-2-2000000002222-222-2220000-2-2-2-2-2-2-222-2-22200000000-2000-2000002200000000000000000000
χ3922222222-2-2-2000000002222-2-2-2-2-2-20000-22222-2-222-2-222000000002000200000-2-200000000000000000000
χ4022222222-2-2-2000000002222-2-2-2-2-2-20000-2-2-2-2-222-2-222-2-20000000020002000002200000000000000000000
χ412222-2-2-2-222-20000000022-2-2-2222-2-20000-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000002000-200000−2i2i00000000000000000000
χ422222-2-2-2-222-20000000022-2-2-2222-2-20000-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000002000-2000002i−2i00000000000000000000
χ432222-2-2-2-222-20000000022-2-2-2-2-22220000-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000-2000200000−2i2i00000000000000000000
χ442222-2-2-2-222-20000000022-2-2-2-2-22220000-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000-20002000002i−2i00000000000000000000
χ452222-2-2-2-2-2-222i2i2i2i−2i−2i−2i−2i-2-222200200−2i−2i2i2i-20000000000000000000002-220-2000000−2i2i2i−2i0000000000000000
χ462222-2-2-2-2-2-222i2i2i2i−2i−2i−2i−2i-2-222200200−2i−2i2i2i-2000000000000000000000-22-2020000002i−2i−2i2i0000000000000000
χ472222-2-2-2-2-2-22−2i−2i−2i−2i2i2i2i2i-2-2222002002i2i−2i−2i-20000000000000000000002-220-20000002i−2i−2i2i0000000000000000
χ482222-2-2-2-2-2-22−2i−2i−2i−2i2i2i2i2i-2-2222002002i2i−2i−2i-2000000000000000000000-22-202000000−2i2i2i−2i0000000000000000
χ4922-2-22i−2i2i−2i0001+i1+i−1−i−1−i1−i1−i−1+i−1+i2-22i−2i02-202i−2i1+i−1−i1−i−1+i02ζ−2ζ2ζ3−2ζ32ζ−2ζ002ζ3−2ζ30022−2−2i2i2−i2−i20000001+i−1−i1−i−1+i0000002−2i2−i2000000000000
χ5022-2-22i−2i2i−2i0001+i1+i−1−i−1−i1−i1−i−1+i−1+i2-22i−2i02-202i−2i1+i−1−i1−i−1+i0−2ζ2ζ−2ζ32ζ3−2ζ2ζ00−2ζ32ζ300−2−222−i2−i2i2i20000001+i−1−i1−i−1+i000000−22−i2i2000000000000
χ5122-2-22i−2i2i−2i0001+i1+i−1−i−1−i1−i1−i−1+i−1+i2-22i−2i0-220−2i2i1+i−1−i1−i−1+i02ζ−2ζ2ζ3−2ζ3−2ζ2ζ00−2ζ32ζ300−2−222−i2−i2i2i2000000−1−i1+i−1+i1−i0000002−2i2−i2000000000000
χ5222-2-22i−2i2i−2i0001+i1+i−1−i−1−i1−i1−i−1+i−1+i2-22i−2i0-220−2i2i1+i−1−i1−i−1+i0−2ζ2ζ−2ζ32ζ32ζ−2ζ002ζ3−2ζ30022−2−2i2i2−i2−i2000000−1−i1+i−1+i1−i000000−22−i2i2000000000000
χ5322-2-22i−2i2i−2i000−1−i−1−i1+i1+i−1+i−1+i1−i1−i2-22i−2i02-202i−2i−1−i1+i−1+i1−i02ζ−2ζ2ζ3−2ζ32ζ−2ζ002ζ3−2ζ300−2−222−i2−i2i2i2000000−1−i1+i−1+i1−i000000−22−i2i2000000000000
χ5422-2-22i−2i2i−2i000−1−i−1−i1+i1+i−1+i−1+i1−i1−i2-22i−2i02-202i−2i−1−i1+i−1+i1−i0−2ζ2ζ−2ζ32ζ3−2ζ2ζ00−2ζ32ζ30022−2−2i2i2−i2−i2000000−1−i1+i−1+i1−i0000002−2i2−i2000000000000
χ5522-2-22i−2i2i−2i000−1−i−1−i1+i1+i−1+i−1+i1−i1−i2-22i−2i0-220−2i2i−1−i1+i−1+i1−i02ζ−2ζ2ζ3−2ζ3−2ζ2ζ00−2ζ32ζ30022−2−2i2i2−i2−i20000001+i−1−i1−i−1+i000000−22−i2i2000000000000
χ5622-2-22i−2i2i−2i000−1−i−1−i1+i1+i−1+i−1+i1−i1−i2-22i−2i0-220−2i2i−1−i1+i−1+i1−i0−2ζ2ζ−2ζ32ζ32ζ−2ζ002ζ3−2ζ300−2−222−i2−i2i2i20000001+i−1−i1−i−1+i0000002−2i2−i2000000000000
χ5722-2-2−2i2i−2i2i0001−i1−i−1+i−1+i1+i1+i−1−i−1−i2-2−2i2i02-20−2i2i1−i−1+i1+i−1−i02ζ3−2ζ32ζ−2ζ2ζ3−2ζ3002ζ−2ζ00−2−222i2i2−i2−i20000001−i−1+i1+i−1−i000000−22i2−i2000000000000
χ5822-2-2−2i2i−2i2i0001−i1−i−1+i−1+i1+i1+i−1−i−1−i2-2−2i2i02-20−2i2i1−i−1+i1+i−1−i0−2ζ32ζ3−2ζ2ζ−2ζ32ζ300−2ζ2ζ0022−2−2−i2−i2i2i20000001−i−1+i1+i−1−i0000002−2−i2i2000000000000
χ5922-2-2−2i2i−2i2i0001−i1−i−1+i−1+i1+i1+i−1−i−1−i2-2−2i2i0-2202i−2i1−i−1+i1+i−1−i02ζ3−2ζ32ζ−2ζ−2ζ32ζ300−2ζ2ζ0022−2−2−i2−i2i2i2000000−1+i1−i−1−i1+i000000−22i2−i2000000000000
χ6022-2-2−2i2i−2i2i0001−i1−i−1+i−1+i1+i1+i−1−i−1−i2-2−2i2i0-2202i−2i1−i−1+i1+i−1−i0−2ζ32ζ3−2ζ2ζ2ζ3−2ζ3002ζ−2ζ00−2−222i2i2−i2−i2000000−1+i1−i−1−i1+i0000002−2−i2i2000000000000
χ6122-2-2−2i2i−2i2i000−1+i−1+i1−i1−i−1−i−1−i1+i1+i2-2−2i2i02-20−2i2i−1+i1−i−1−i1+i02ζ3−2ζ32ζ−2ζ2ζ3−2ζ3002ζ−2ζ0022−2−2−i2−i2i2i2000000−1+i1−i−1−i1+i0000002−2−i2i2000000000000
χ6222-2-2−2i2i−2i2i000−1+i−1+i1−i1−i−1−i−1−i1+i1+i2-2−2i2i02-20−2i2i−1+i1−i−1−i1+i0−2ζ32ζ3−2ζ2ζ−2ζ32ζ300−2ζ2ζ00−2−222i2i2−i2−i2000000−1+i1−i−1−i1+i000000−22i2−i2000000000000
χ6322-2-2−2i2i−2i2i000−1+i−1+i1−i1−i−1−i−1−i1+i1+i2-2−2i2i0-2202i−2i−1+i1−i−1−i1+i02ζ3−2ζ32ζ−2ζ−2ζ32ζ300−2ζ2ζ00−2−222i2i2−i2−i20000001−i−1+i1+i−1−i0000002−2−i2i2000000000000
χ6422-2-2−2i2i−2i2i000−1+i−1+i1−i1−i−1−i−1−i1+i1+i2-2−2i2i0-2202i−2i−1+i1−i−1−i1+i0−2ζ32ζ3−2ζ2ζ2ζ3−2ζ3002ζ−2ζ0022−2−2−i2−i2i2i20000001−i−1+i1+i−1−i000000−22i2−i2000000000000
χ6544444444-4-4-400000000-4-4-4-4-400400000040000000000000000000000000000000000000000000000000000
χ664444-4-4-4-444-400000000-4-444-400-400000040000000000000000000000000000000000000000000000000000
χ6744-4-44i−4i4i−4i0002+2i2+2i−2−2i−2−2i2−2i2−2i−2+2i−2+2i-44−4i4i000000−2−2i2+2i−2+2i2−2i00000000000000000000000000000000000000000000000000000
χ6844-4-44i−4i4i−4i000−2−2i−2−2i2+2i2+2i−2+2i−2+2i2−2i2−2i-44−4i4i0000002+2i−2−2i2−2i−2+2i00000000000000000000000000000000000000000000000000000
χ6944-4-4−4i4i−4i4i0002−2i2−2i−2+2i−2+2i2+2i2+2i−2−2i−2−2i-444i−4i000000−2+2i2−2i−2−2i2+2i00000000000000000000000000000000000000000000000000000
χ7044-4-4−4i4i−4i4i000−2+2i−2+2i2−2i2−2i−2−2i−2−2i2+2i2+2i-444i−4i0000002−2i−2+2i2+2i−2−2i00000000000000000000000000000000000000000000000000000
χ714-44-44i−4i−4i4i0002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i0000000000000000000002−2i−2+2i002+2i−2−2i2-22-22i−2i2i−2i00000000000000000000000000000000
χ724-44-44i−4i−4i4i0002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i000000000000000000000−2+2i2−2i00−2−2i2+2i-22-22−2i2i−2i2i00000000000000000000000000000000
χ734-44-44i−4i−4i4i000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i0000000000000000000002−2i−2+2i002+2i−2−2i-22-22−2i2i−2i2i00000000000000000000000000000000
χ744-44-44i−4i−4i4i000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i000000000000000000000−2+2i2−2i00−2−2i2+2i2-22-22i−2i2i−2i00000000000000000000000000000000
χ754-44-4−4i4i4i−4i0002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i0000000000000000000002+2i−2−2i002−2i−2+2i2-22-2−2i2i−2i2i00000000000000000000000000000000
χ764-44-4−4i4i4i−4i0002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i000000000000000000000−2−2i2+2i00−2+2i2−2i-22-222i−2i2i−2i00000000000000000000000000000000
χ774-44-4−4i4i4i−4i000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i0000000000000000000002+2i−2−2i002−2i−2+2i-22-222i−2i2i−2i00000000000000000000000000000000
χ784-44-4−4i4i4i−4i000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i000000000000000000000−2−2i2+2i00−2+2i2−2i2-22-2−2i2i−2i2i00000000000000000000000000000000
χ794-4-4444-4-44-444i−4i−4i4i−4i4i4i−4i0000-400000000000000000000000000000000000000000000000000000000000000
χ804-4-4444-4-44-44−4i4i4i−4i4i−4i−4i4i0000-400000000000000000000000000000000000000000000000000000000000000
χ814-4-4444-4-4-44-40000000000004000000000000000000000022−22−222222−22−222200000000000000000000000000000000
χ824-4-4444-4-4-44-400000000000040000000000000000000000−222222−22−222222−2200000000000000000000000000000000
χ834-4-44-4-4444-4-40000000000004000000000000000000000022−22−2222−222222−2200000000000000000000000000000000
χ844-4-44-4-4444-4-400000000000040000000000000000000000−222222−2222−22−222200000000000000000000000000000000
χ854-4-44-4-444-4444-4-444-4-440000-400000000000000000000000000000000000000000000000000000000000000
χ864-4-44-4-444-444-444-4-444-40000-400000000000000000000000000000000000000000000000000000000000000

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