Finite Group Databasebeta

← Group #376149

Character table — Group #376149

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222444444444444448888888888888888888888888888888888888888888816161616
order12224444222222444444888888888888888888222222444444444444444444888888888888888888884488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111
χ171111-1-1-1-11-1-11-1-111-111-1ii−i−iiii−i−i−iiiii−i−i−i−i111-11111-1-1-1-11-1-1-1ii−i−i11-1-1ii−i−iii−i−iii−i−i11-1-1ii−i−ii−i1-1
χ181111-1-1-1-11-1-11-1-111-111-1ii−i−iiii−i−i−iiiii−i−i−i−i111-1-1-111-1-1-1-11-111−i−iii-1-111−i−iiiii−i−iii−i−i-1-111−i−iii−ii-11
χ191111-1-1-1-11-1-11-1-111-111-1ii−i−iiii−i−i−iiiii−i−i−i−i-1-1-111111-1-111-11-1-1ii−i−i-1-111ii−i−i−i−iii−i−iii11-1-1−i−iii−ii-11
χ201111-1-1-1-11-1-11-1-111-111-1ii−i−iiii−i−i−iiiii−i−i−i−i-1-1-11-1-111-1-111-1111−i−iii11-1-1−i−iii−i−iii−i−iii-1-111ii−i−ii−i1-1
χ211111-1-1-1-11-1-11-1-111-111-1ii−i−iiii−i−i−i−i−i−i−iiiii11-1111-1-111-1-1-11-1-1−i−iii11-1-1ii−i−iii−i−i−i−iii-1-111ii−i−i−ii-11
χ221111-1-1-1-11-1-11-1-111-111-1ii−i−iiii−i−i−i−i−i−i−iiiii11-11-1-1-1-111-1-1-1111ii−i−i-1-111−i−iiiii−i−i−i−iii11-1-1−i−iiii−i1-1
χ231111-1-1-1-11-1-11-1-111-111-1ii−i−iiii−i−i−i−i−i−i−iiiii-1-11-111-1-111111-1-1-1−i−iii-1-111ii−i−i−i−iiiii−i−i-1-111−i−iiii−i1-1
χ241111-1-1-1-11-1-11-1-111-111-1ii−i−iiii−i−i−i−i−i−i−iiiii-1-11-1-1-1-1-111111-111ii−i−i11-1-1−i−iii−i−iiiii−i−i11-1-1ii−i−i−ii-11
χ251111-1-1-1-11-1-11-1-111-111-1−i−iii−i−i−iiiiiiii−i−i−i−i11-1111-1-111-1-1-11-1-1ii−i−i11-1-1−i−iii−i−iiiii−i−i-1-111−i−iiii−i-11
χ261111-1-1-1-11-1-11-1-111-111-1−i−iii−i−i−iiiiiiii−i−i−i−i11-11-1-1-1-111-1-1-1111−i−iii-1-111ii−i−i−i−iiiii−i−i11-1-1ii−i−i−ii1-1
χ271111-1-1-1-11-1-11-1-111-111-1−i−iii−i−i−iiiiiiii−i−i−i−i-1-11-111-1-111111-1-1-1ii−i−i-1-111−i−iiiii−i−i−i−iii-1-111ii−i−i−ii1-1
χ281111-1-1-1-11-1-11-1-111-111-1−i−iii−i−i−iiiiiiii−i−i−i−i-1-11-1-1-1-1-111111-111−i−iii11-1-1ii−i−iii−i−i−i−iii11-1-1−i−iiii−i-11
χ291111-1-1-1-11-1-11-1-111-111-1−i−iii−i−i−iiii−i−i−i−iiiii111-11111-1-1-1-11-1-1-1−i−iii11-1-1−i−iii−i−iii−i−iii11-1-1−i−iii−ii1-1
χ301111-1-1-1-11-1-11-1-111-111-1−i−iii−i−i−iiii−i−i−i−iiiii111-1-1-111-1-1-1-11-111ii−i−i-1-111ii−i−i−i−iii−i−iii-1-111ii−i−ii−i-11
χ311111-1-1-1-11-1-11-1-111-111-1−i−iii−i−i−iiii−i−i−i−iiiii-1-1-111111-1-111-11-1-1−i−iii-1-111−i−iiiii−i−iii−i−i11-1-1ii−i−ii−i-11
χ321111-1-1-1-11-1-11-1-111-111-1−i−iii−i−i−iiii−i−i−i−iiiii-1-1-11-1-111-1-111-1111ii−i−i11-1-1ii−i−iii−i−iii−i−i-1-111−i−iii−ii1-1
χ33222222222-2-22-2-2-2-22-2-2222222-2-22-2-2000000002-2000000002-200000000000000002-22-20000000000000000
χ34222222222-2-22-2-2-2-22-2-2222222-2-22-2-200000000-2200000000-220000000000000000-22-220000000000000000
χ35222222222-2-22-2-2-2-22-2-22-2-2-2-2-222-222000000002-2000000002-20000000000000000-22-220000000000000000
χ36222222222-2-22-2-2-2-22-2-22-2-2-2-2-222-22200000000-2200000000-2200000000000000002-22-20000000000000000
χ3722222222-22-2-22-22-2-22-2-22222-22-2-22-200000000002-200000000-220000000000000000002-22-2000000000000
χ3822222222-22-2-22-22-2-22-2-22222-22-2-22-20000000000-22000000002-2000000000000000000-22-22000000000000
χ3922222222-22-2-22-22-2-22-2-2-2-2-2-22-222-2200000000002-200000000-22000000000000000000-22-22000000000000
χ4022222222-22-2-22-22-2-22-2-2-2-2-2-22-222-220000000000-22000000002-20000000000000000002-22-2000000000000
χ4122222222-2-22-2-22-22-2-22-22222-2-22-2-2222-2-222-2-20000002-22-200000000000000000000000000000000000000
χ4222222222-2-22-2-22-22-2-22-22222-2-22-2-22-2-222-2-222000000-22-2200000000000000000000000000000000000000
χ4322222222-2-22-2-22-22-2-22-2-2-2-2-222-222-222-2-222-2-2000000-22-2200000000000000000000000000000000000000
χ4422222222-2-22-2-22-22-2-22-2-2-2-2-222-222-2-2-222-2-2220000002-22-200000000000000000000000000000000000000
χ452222-2-2-2-2222222-2-2-2-2-2-22i2i−2i−2i2i−2i−2i−2i2i2i000000002-200000000-2200000000000000002i−2i−2i2i0000000000000000
χ462222-2-2-2-2222222-2-2-2-2-2-22i2i−2i−2i2i−2i−2i−2i2i2i00000000-22000000002-20000000000000000−2i2i2i−2i0000000000000000
χ472222-2-2-2-2222222-2-2-2-2-2-2−2i−2i2i2i−2i2i2i2i−2i−2i000000002-200000000-220000000000000000−2i2i2i−2i0000000000000000
χ482222-2-2-2-2222222-2-2-2-2-2-2−2i−2i2i2i−2i2i2i2i−2i−2i00000000-22000000002-200000000000000002i−2i−2i2i0000000000000000
χ492222-2-2-2-2-22-2-22-2-222-2222i2i−2i−2i−2i−2i2i2i2i−2i2i2i−2i−2i−2i−2i2i2i0000002-2-2200000000000000000000000000000000000000
χ502222-2-2-2-2-22-2-22-2-222-2222i2i−2i−2i−2i−2i2i2i2i−2i−2i−2i2i2i2i2i−2i−2i000000-222-200000000000000000000000000000000000000
χ512222-2-2-2-2-22-2-22-2-222-222−2i−2i2i2i2i2i−2i−2i−2i2i2i2i−2i−2i−2i−2i2i2i000000-222-200000000000000000000000000000000000000
χ522222-2-2-2-2-22-2-22-2-222-222−2i−2i2i2i2i2i−2i−2i−2i2i−2i−2i2i2i2i2i−2i−2i0000002-2-2200000000000000000000000000000000000000
χ532222-2-2-2-2-2-22-2-222-222-222i2i−2i−2i−2i2i−2i2i−2i2i00000000002200000000-2-20000000000000000002i−2i−2i2i000000000000
χ542222-2-2-2-2-2-22-2-222-222-222i2i−2i−2i−2i2i−2i2i−2i2i0000000000-2-20000000022000000000000000000−2i2i2i−2i000000000000
χ552222-2-2-2-2-2-22-2-222-222-22−2i−2i2i2i2i−2i2i−2i2i−2i00000000002200000000-2-2000000000000000000−2i2i2i−2i000000000000
χ562222-2-2-2-2-2-22-2-222-222-22−2i−2i2i2i2i−2i2i−2i2i−2i0000000000-2-200000000220000000000000000002i−2i−2i2i000000000000
χ572-2-2222-2-22-22-22-222-2-2-2200000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000002-22-2000000002i−2i2i−2i00000000
χ582-2-2222-2-22-22-22-222-2-2-2200000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000-22-2200000000−2i2i−2i2i00000000
χ592-2-2222-2-22-22-22-222-2-2-220000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000002-22-200000000−2i2i−2i2i00000000
χ602-2-2222-2-22-22-22-222-2-2-220000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000-22-22000000002i−2i2i−2i00000000
χ612-2-2222-2-2-2222-2-2-2222-2-200000000002i−2i−2i2i2i−2i−2i2i00002-2000000002-22i−2i2i−2i0000000000000000000000000000
χ622-2-2222-2-2-2222-2-2-2222-2-200000000002i−2i−2i2i2i−2i−2i2i0000-2200000000-22−2i2i−2i2i0000000000000000000000000000
χ632-2-2222-2-2-2222-2-2-2222-2-20000000000−2i2i2i−2i−2i2i2i−2i00002-2000000002-2−2i2i−2i2i0000000000000000000000000000
χ642-2-2222-2-2-2222-2-2-2222-2-20000000000−2i2i2i−2i−2i2i2i−2i0000-2200000000-222i−2i2i−2i0000000000000000000000000000
χ652-2-22-2-22222-2-2-22222-2-2-200000000002-22-2-22-220000000000000000000000002i−2i−2i2i00000000−2i2i2i−2i00000000
χ662-2-22-2-22222-2-2-22222-2-2-200000000002-22-2-22-22000000000000000000000000−2i2i2i−2i000000002i−2i−2i2i00000000
χ672-2-22-2-22222-2-2-22222-2-2-20000000000-22-222-22-20000000000000000000000002i−2i−2i2i000000002i−2i−2i2i00000000
χ682-2-22-2-22222-2-2-22222-2-2-20000000000-22-222-22-2000000000000000000000000−2i2i2i−2i00000000−2i2i2i−2i00000000
χ692-2-22-2-222-2-2-2222-22-22-2200000000002-2-22-222-200002-200000000-222-2-220000000000000000000000000000
χ702-2-22-2-222-2-2-2222-22-22-2200000000002-2-22-222-20000-22000000002-2-222-20000000000000000000000000000
χ712-2-22-2-222-2-2-2222-22-22-220000000000-222-22-2-2200002-200000000-22-222-20000000000000000000000000000
χ722-2-22-2-222-2-2-2222-22-22-220000000000-222-22-2-220000-22000000002-22-2-220000000000000000000000000000
χ7344-4-44i−4i4i−4i0000000000004ζ−4ζ4ζ3−4ζ300000000000000000000000000000000002-22i−2i00000000000000002ζ−2ζ2ζ3−2ζ30000
χ7444-4-44i−4i4i−4i0000000000004ζ−4ζ4ζ3−4ζ30000000000000000000000000000000000-22−2i2i0000000000000000−2ζ2ζ−2ζ32ζ30000
χ7544-4-44i−4i4i−4i000000000000−4ζ4ζ−4ζ34ζ300000000000000000000000000000000002-22i−2i0000000000000000−2ζ2ζ−2ζ32ζ30000
χ7644-4-44i−4i4i−4i000000000000−4ζ4ζ−4ζ34ζ30000000000000000000000000000000000-22−2i2i00000000000000002ζ−2ζ2ζ3−2ζ30000
χ7744-4-4−4i4i−4i4i0000000000004ζ3−4ζ34ζ−4ζ00000000000000000000000000000000002-2−2i2i00000000000000002ζ3−2ζ32ζ−2ζ0000
χ7844-4-4−4i4i−4i4i0000000000004ζ3−4ζ34ζ−4ζ0000000000000000000000000000000000-222i−2i0000000000000000−2ζ32ζ3−2ζ2ζ0000
χ7944-4-4−4i4i−4i4i000000000000−4ζ34ζ3−4ζ4ζ00000000000000000000000000000000002-2−2i2i0000000000000000−2ζ32ζ3−2ζ2ζ0000
χ8044-4-4−4i4i−4i4i000000000000−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000-222i−2i00000000000000002ζ3−2ζ32ζ−2ζ0000
χ814-4-4444-4-444-4-4-44-4-4-4444000000000000000000000000000000000000000000000000000000000000000000
χ824-4-4444-4-4-4-4-44444-44-44-4000000000000000000000000000000000000000000000000000000000000000000
χ834-4-44-4-4444-44-44-4-4-4444-4000000000000000000000000000000000000000000000000000000000000000000
χ844-4-44-4-444-4444-4-44-4-4-444000000000000000000000000000000000000000000000000000000000000000000
χ858-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000000000

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