Finite Group Databasebeta

← Group #208751

Character table — Group #208751

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12224444224444444444888888884444444444444444888888888888224444444444888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-11-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-11-11-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-1111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111111-1-111-1-111-1-1-1-11111-1-1111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-111-1-1-1-11111111111-1-11111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-11111-1-11111111111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1111111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-111111-1-11111-1-11111-1-1-1-111-1-111-1-1-1-111
χ171111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i11-1-111-1-11-11-1i−ii−iii−i−iii−i−ii−ii−i1-1i−i1-1i−i
χ181111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i-1-11111-1-1-11-11−ii−iiii−i−iii−i−i−ii−ii-11−ii-11−ii
χ191111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1-1-1-1-11111ii−i−i−i−i−i−iiiii11-1-1-1-1111-11-1i−ii−iii−i−i−i−iiii−ii−i-11−ii-11−ii
χ201111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1-1-1-1-11111ii−i−i−i−i−i−iiiii-1-111-1-111-11-11−ii−iiii−i−i−i−iii−ii−ii1-1i−i1-1i−i
χ211111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-111111111-1-1-1-1ii−i−iiiii−i−i−i−i1-1-11-1-1111-1-11i−i−ii−i−iii−i−iiii−i−ii1-1i−i-11−ii
χ221111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-111111111-1-1-1-1ii−i−iiiii−i−i−i−i-111-1-1-111-111-1−iii−i−i−iii−i−iii−iii−i-11−ii1-1i−i
χ231111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-11111-1-1-1-11111ii−i−i−i−i−i−iiiii1-1-1111-1-11-1-11i−i−ii−i−iiiii−i−ii−i−ii-11−ii1-1i−i
χ241111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-11111-1-1-1-11111ii−i−i−i−i−i−iiiii-111-111-1-1-111-1−iii−i−i−iiiii−i−i−iii−i1-1i−i-11−ii
χ251111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−i−i−iiiii11-1-111-1-11-11-1−ii−ii−i−iii−i−iii−ii−ii1-1−ii1-1−ii
χ261111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−i−i−iiiii-1-11111-1-1-11-11i−ii−i−i−iii−i−iiii−ii−i-11i−i-11i−i
χ271111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−i−iiiiiii−i−i−i−i11-1-1-1-1111-11-1−ii−ii−i−iiiii−i−i−ii−ii-11i−i-11i−i
χ281111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−i−iiiiiii−i−i−i−i-1-111-1-111-11-11i−ii−i−i−iiiii−i−ii−ii−i1-1−ii1-1−ii
χ291111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−iii−i−i−i−iiiii1-1-11-1-1111-1-11−iii−iii−i−iii−i−i−iii−i1-1−ii-11i−i
χ301111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−iii−i−i−i−iiiii-111-1-1-111-111-1i−i−iiii−i−iii−i−ii−i−ii-11i−i1-1−ii
χ311111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-11111-1-1-1-11111−i−iiiiiii−i−i−i−i1-1-1111-1-11-1-11−iii−iii−i−i−i−iii−iii−i-11i−i1-1−ii
χ321111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-11111-1-1-1-11111−i−iiiiiii−i−i−i−i-111-111-1-1-111-1i−i−iiii−i−i−i−iiii−i−ii1-1−ii-11i−i
χ33222222222222-2-2-2-2-2-2-2-22222222222-2-222-2-200000000-2-2-2-20000000000000000000000002-22-20000000000000000
χ34222222222222-2-2-2-2-2-2-2-222222222-2-222-2-22200000000-2-2-2-2000000000000000000000000-22-220000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-2000000002222000000000000000000000000-22-220000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2220000000022220000000000000000000000002-22-20000000000000000
χ3722222222-2-2-2-222-2-222-2-222-2-222-2-200000000000000002-22-2000000000202000000-2-200220000000000-2-200000000
χ3822222222-2-2-2-222-2-222-2-222-2-222-2-200000000000000002-22-2000000000-20-20000002200-2-200000000002200000000
χ3922222222-2-2-2-222-2-222-2-2-2-222-2-2220000000000000000-22-22000000000202000000-2-200-2-200000000002200000000
χ4022222222-2-2-2-222-2-222-2-2-2-222-2-2220000000000000000-22-22000000000-20-20000002200220000000000-2-200000000
χ4122222222-2-2-2-2-2-222-2-22222-2-222-2-20000000000000000-22-220000000020200000-2-200220000000000-2-20000000000
χ4222222222-2-2-2-2-2-222-2-22222-2-222-2-20000000000000000-22-2200000000-20-2000002200-2-20000000000220000000000
χ4322222222-2-2-2-2-2-222-2-222-2-222-2-22200000000000000002-22-20000000020200000-2-200-2-20000000000220000000000
χ4422222222-2-2-2-2-2-222-2-222-2-222-2-22200000000000000002-22-200000000-20-2000002200220000000000-2-20000000000
χ452222-2-2-2-222-2-2-2-2-2-222222i2i2i2i−2i−2i−2i−2i22-2-2-2-22200000000−2i−2i2i2i0000000000000000000000002i−2i−2i2i0000000000000000
χ462222-2-2-2-222-2-2-2-2-2-222222i2i2i2i−2i−2i−2i−2i-2-22222-2-200000000−2i−2i2i2i000000000000000000000000−2i2i2i−2i0000000000000000
χ472222-2-2-2-222-2-2-2-2-2-22222−2i−2i−2i−2i2i2i2i2i22-2-2-2-222000000002i2i−2i−2i000000000000000000000000−2i2i2i−2i0000000000000000
χ482222-2-2-2-222-2-2-2-2-2-22222−2i−2i−2i−2i2i2i2i2i-2-22222-2-2000000002i2i−2i−2i0000000000000000000000002i−2i−2i2i0000000000000000
χ492222-2-2-2-2-2-22222-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000000000002i−2i−2i2i00000000020-2000000-22002i−2i0000000000−2i2i00000000
χ502222-2-2-2-2-2-22222-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000000000002i−2i−2i2i000000000-2020000002-200−2i2i00000000002i−2i00000000
χ512222-2-2-2-2-2-22222-2-2-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000−2i2i2i−2i00000000020-2000000-2200−2i2i00000000002i−2i00000000
χ522222-2-2-2-2-2-22222-2-2-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000−2i2i2i−2i000000000-2020000002-2002i−2i0000000000−2i2i00000000
χ532222-2-2-2-2-2-222-2-22222-2-22i2i−2i−2i−2i−2i2i2i0000000000000000−2i2i2i−2i0000000020-200000-22002i−2i0000000000−2i2i0000000000
χ542222-2-2-2-2-2-222-2-22222-2-22i2i−2i−2i−2i−2i2i2i0000000000000000−2i2i2i−2i00000000-202000002-200−2i2i00000000002i−2i0000000000
χ552222-2-2-2-2-2-222-2-22222-2-2−2i−2i2i2i2i2i−2i−2i00000000000000002i−2i−2i2i0000000020-200000-2200−2i2i00000000002i−2i0000000000
χ562222-2-2-2-2-2-222-2-22222-2-2−2i−2i2i2i2i2i−2i−2i00000000000000002i−2i−2i2i00000000-202000002-2002i−2i0000000000−2i2i0000000000
χ572-22-22i−2i2i−2i2-22i−2i2-22-22i−2i2i−2i000000002-22-22i−2i2i−2i0000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000000000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ582-22-22i−2i2i−2i2-22i−2i2-22-22i−2i2i−2i000000002-22-22i−2i2i−2i000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ592-22-22i−2i2i−2i2-22i−2i2-22-22i−2i2i−2i00000000-22-22−2i2i−2i2i0000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ602-22-22i−2i2i−2i2-22i−2i2-22-22i−2i2i−2i00000000-22-22−2i2i−2i2i000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000000000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ612-22-22i−2i2i−2i2-22i−2i-22-22−2i2i−2i2i000000002-2-222i−2i−2i2i22-2-22i2i−2i−2i00000000000000002-22i−2i0000000000000000000000000000
χ622-22-22i−2i2i−2i2-22i−2i-22-22−2i2i−2i2i000000002-2-222i−2i−2i2i-2-222−2i−2i2i2i0000000000000000-22−2i2i0000000000000000000000000000
χ632-22-22i−2i2i−2i2-22i−2i-22-22−2i2i−2i2i00000000-222-2−2i2i2i−2i22-2-22i2i−2i−2i0000000000000000-22−2i2i0000000000000000000000000000
χ642-22-22i−2i2i−2i2-22i−2i-22-22−2i2i−2i2i00000000-222-2−2i2i2i−2i-2-222−2i−2i2i2i00000000000000002-22i−2i0000000000000000000000000000
χ652-22-2−2i2i−2i2i2-2−2i2i2-22-2−2i2i−2i2i000000002-22-2−2i2i−2i2i0000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000000000000000002ζ3−2ζ32ζ−2ζ000000000000
χ662-22-2−2i2i−2i2i2-2−2i2i2-22-2−2i2i−2i2i000000002-22-2−2i2i−2i2i000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ672-22-2−2i2i−2i2i2-2−2i2i2-22-2−2i2i−2i2i00000000-22-222i−2i2i−2i0000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ682-22-2−2i2i−2i2i2-2−2i2i2-22-2−2i2i−2i2i00000000-22-222i−2i2i−2i000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000000000000000002ζ3−2ζ32ζ−2ζ000000000000
χ692-22-2−2i2i−2i2i2-2−2i2i-22-222i−2i2i−2i000000002-2-22−2i2i2i−2i22-2-2−2i−2i2i2i00000000000000002-2−2i2i0000000000000000000000000000
χ702-22-2−2i2i−2i2i2-2−2i2i-22-222i−2i2i−2i000000002-2-22−2i2i2i−2i-2-2222i2i−2i−2i0000000000000000-222i−2i0000000000000000000000000000
χ712-22-2−2i2i−2i2i2-2−2i2i-22-222i−2i2i−2i00000000-222-22i−2i−2i2i22-2-2−2i−2i2i2i0000000000000000-222i−2i0000000000000000000000000000
χ722-22-2−2i2i−2i2i2-2−2i2i-22-222i−2i2i−2i00000000-222-22i−2i−2i2i-2-2222i2i−2i−2i00000000000000002-2−2i2i0000000000000000000000000000
χ7344-4-444-4-40000000000004-4004-400000000002-22-22-22-200002-22-22-22-2000000000000000000000000000000000000
χ7444-4-444-4-40000000000004-4004-40000000000-22-22-22-220000-22-22-22-22000000000000000000000000000000000000
χ7544-4-444-4-4000000000000-4400-4400000000002-22-22-22-20000-22-22-22-22000000000000000000000000000000000000
χ7644-4-444-4-4000000000000-4400-440000000000-22-22-22-2200002-22-22-22-2000000000000000000000000000000000000
χ7744-4-4-4-4440000000000004i−4i00−4i4i00000000002-22-2-22-2200002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ7844-4-4-4-4440000000000004i−4i00−4i4i0000000000-22-222-22-20000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ7944-4-4-4-444000000000000−4i4i004i−4i00000000002-22-2-22-220000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ8044-4-4-4-444000000000000−4i4i004i−4i0000000000-22-222-22-200002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ814-44-44i−4i4i−4i-44−4i4i4-4-444i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ824-44-44i−4i4i−4i-44−4i4i-444-4−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ834-44-4−4i4i−4i4i-444i−4i4-4-44−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ844-44-4−4i4i−4i4i-444i−4i-444-44i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ854-4-444i−4i−4i4i000000000000004ζ−4ζ004ζ3−4ζ3000000002-2-222i−2i−2i2i00002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000000000000000
χ864-4-444i−4i−4i4i000000000000004ζ−4ζ004ζ3−4ζ300000000-222-2−2i2i2i−2i0000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000000000000000
χ874-4-444i−4i−4i4i00000000000000−4ζ4ζ00−4ζ34ζ3000000002-2-222i−2i−2i2i0000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000000000000000
χ884-4-444i−4i−4i4i00000000000000−4ζ4ζ00−4ζ34ζ300000000-222-2−2i2i2i−2i00002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000000000000000
χ894-4-44−4i4i4i−4i000000000000004ζ3−4ζ3004ζ−4ζ000000002-2-22−2i2i2i−2i00002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000000000000000
χ904-4-44−4i4i4i−4i000000000000004ζ3−4ζ3004ζ−4ζ00000000-222-22i−2i−2i2i0000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000000000000000
χ914-4-44−4i4i4i−4i00000000000000−4ζ34ζ300−4ζ4ζ000000002-2-22−2i2i2i−2i0000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000000000000000
χ924-4-44−4i4i4i−4i00000000000000−4ζ34ζ300−4ζ4ζ00000000-222-22i−2i−2i2i00002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000000000000000

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