Finite Group Databasebeta

← Group #199166

Character table — Group #199166

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222244444444444444444444444444488881616161616161111222222224444444444444444444444444448888161616161616
order12222244444444444444444888888888888888888884444882222224444444444444444488888888888888888888444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ61111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ81111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ91111-1-11-11-1-1-1111-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i1-1i−i1-11111-1-11-11-1-1-1111-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i1-1i−i1-1
χ101111-1-11-11-1-1-1111-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii-11−ii-111111-1-11-11-1-1-1111-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii-11−ii-11
χ111111-1-11-11-1-1-1111-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i-11i−i-111111-1-11-11-1-1-1111-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i-11i−i-11
χ121111-1-11-11-1-1-1111-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii1-1−ii1-11111-1-11-11-1-1-1111-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii1-1−ii1-1
χ131111-1-11-11-1-1-11-1-1111-1-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i1-1−ii-111111-1-11-11-1-1-11-1-1111-1-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i1-1−ii-11
χ141111-1-11-11-1-1-11-1-1111-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iii-11i−i1-11111-1-11-11-1-1-11-1-1111-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iii-11i−i1-1
χ151111-1-11-11-1-1-11-1-1111-1-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i-11−ii1-11111-1-11-11-1-1-11-1-1111-1-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i-11−ii1-1
χ161111-1-11-11-1-1-11-1-1111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iii1-1i−i-111111-1-11-11-1-1-11-1-1111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iii1-1i−i-11
χ172222222222-2-2-22222-2-2-2-2-2-2000000000000000000000000002222222222-2-2-22222-2-2-2-2-2-200000000000000000000000000
χ182222222222-2-2-2-2-2-2-2-2-22222000000000000000000000000002222222222-2-2-2-2-2-2-2-2-2222200000000000000000000000000
χ19222222-2-2-2-22220000-2-200000000000022-2-222-2-20000000000222222-2-2-2-22220000-2-200000000000022-2-222-2-20000000000
χ20222222-2-2-2-22220000-2-2000000000000-2-222-2-2220000000000222222-2-2-2-22220000-2-2000000000000-2-222-2-2220000000000
χ21222222-2-2-2-2-2-2-200002200002i2i−2i−2i2i2i−2i−2i000000000000000000222222-2-2-2-2-2-2-200002200002i2i−2i−2i2i2i−2i−2i000000000000000000
χ22222222-2-2-2-2-2-2-20000220000−2i−2i2i2i−2i−2i2i2i000000000000000000222222-2-2-2-2-2-2-20000220000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ232222-2-22-22-222-222-2-2-22-2-222000000000000000000000000002222-2-22-22-222-222-2-2-22-2-22200000000000000000000000000
χ242222-2-22-22-222-2-2-222-2222-2-2000000000000000000000000002222-2-22-22-222-2-2-222-2222-2-200000000000000000000000000
χ252222-2-2-22-2222-200002-2000022-2-2-2-2220000000000000000002222-2-2-22-2222-200002-2000022-2-2-2-222000000000000000000
χ262222-2-2-22-2222-200002-20000-2-22222-2-20000000000000000002222-2-2-22-2222-200002-20000-2-22222-2-2000000000000000000
χ272222-2-2-22-22-2-220000-220000000000002i2i−2i−2i−2i−2i2i2i00000000002222-2-2-22-22-2-220000-220000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ282222-2-2-22-22-2-220000-22000000000000−2i−2i2i2i2i2i−2i−2i00000000002222-2-2-22-22-2-220000-22000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ2922-2-22-222-2-20002-22-20000002−22−22−22−22−22−22−22−2000000000022-2-22-222-2-20002-22-20000002−22−22−22−22−22−22−22−20000000000
χ3022-2-22-222-2-20002-22-2000000−22−22−22−22−22−22−22−22000000000022-2-22-222-2-20002-22-2000000−22−22−22−22−22−22−22−220000000000
χ3122-2-22-222-2-2000-22-220000002−22−22−22−2−22−22−22−22000000000022-2-22-222-2-2000-22-220000002−22−22−22−2−22−22−22−220000000000
χ3222-2-22-222-2-2000-22-22000000−22−22−22−222−22−22−22−2000000000022-2-22-222-2-2000-22-22000000−22−22−22−222−22−22−22−20000000000
χ3322-2-22-2-2-2220000000002i−2i2i−2ii2−i2−i2i2i2−i2−i2i22−2−222−2−22000000000022-2-22-2-2-2220000000002i−2i2i−2ii2−i2−i2i2i2−i2−i2i22−2−222−2−220000000000
χ3422-2-22-2-2-2220000000002i−2i2i−2i−i2i2i2−i2−i2i2i2−i2−222−2−222−2000000000022-2-22-2-2-2220000000002i−2i2i−2i−i2i2i2−i2−i2i2i2−i2−222−2−222−20000000000
χ3522-2-22-2-2-222000000000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i2−222−2−222−2000000000022-2-22-2-2-222000000000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i2−222−2−222−20000000000
χ3622-2-22-2-2-222000000000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i22−2−222−2−22000000000022-2-22-2-2-222000000000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i22−2−222−2−220000000000
χ3722-2-2-222-2-220002-2-22000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000022-2-2-222-2-220002-2-22000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000
χ3822-2-2-222-2-220002-2-22000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000022-2-2-222-2-220002-2-22000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000
χ3922-2-2-222-2-22000-222-2000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000022-2-2-222-2-22000-222-2000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000
χ4022-2-2-222-2-22000-222-2000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000022-2-2-222-2-22000-222-2000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000
χ4122-2-2-22-222-20000000002i−2i−2i2i2−2−22−222−2−i2i2i2−i2i2−i2−i2i2000000000022-2-2-22-222-20000000002i−2i−2i2i2−2−22−222−2−i2i2i2−i2i2−i2−i2i20000000000
χ4222-2-2-22-222-20000000002i−2i−2i2i−222−22−2−22i2−i2−i2i2−i2i2i2−i2000000000022-2-2-22-222-20000000002i−2i−2i2i−222−22−2−22i2−i2−i2i2−i2i2i2−i20000000000
χ4322-2-2-22-222-2000000000−2i2i2i−2i2−2−22−222−2i2−i2−i2i2−i2i2i2−i2000000000022-2-2-22-222-2000000000−2i2i2i−2i2−2−22−222−2i2−i2−i2i2−i2i2i2−i20000000000
χ4422-2-2-22-222-2000000000−2i2i2i−2i−222−22−2−22−i2i2i2−i2i2−i2−i2i2000000000022-2-2-22-222-2000000000−2i2i2i−2i−222−22−2−22−i2i2i2−i2i2−i2−i2i20000000000
χ454-4-440000004i−4i0000000000000000000000000002ζ3−2ζ32ζ−2ζ0000004-4-440000004i−4i0000000000000000000000000002ζ3−2ζ32ζ−2ζ000000
χ464-4-440000004i−4i000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000004-4-440000004i−4i000000000000000000000000000−2ζ32ζ3−2ζ2ζ000000
χ474-4-44000000−4i4i0000000000000000000000000002ζ−2ζ2ζ3−2ζ30000004-4-44000000−4i4i0000000000000000000000000002ζ−2ζ2ζ3−2ζ3000000
χ484-4-44000000−4i4i000000000000000000000000000−2ζ2ζ−2ζ32ζ30000004-4-44000000−4i4i000000000000000000000000000−2ζ2ζ−2ζ32ζ3000000
χ498-88-80000000000000000000000000000000000000000000008-88-8000000000000000000000000000000000000000000000
χ501111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ5211111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-111
χ5311111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-111-1-1
χ541111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
χ551111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ561111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ571111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ581111-1-11-11-1-1-1111-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i1-1i−i1-1-1-1-1-111-11-1111-1-1-111-11-1-111−i−i−i−iiiii−i−i−i−iiiii−i−iii-11−ii-11
χ591111-1-11-11-1-1-1111-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii-11−ii-11-1-1-1-111-11-1111-1-1-111-11-1-111−i−i−i−iiiii−i−i−i−iiiiiii−i−i1-1i−i1-1
χ601111-1-11-11-1-1-1111-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i-11i−i-11-1-1-1-111-11-1111-1-1-111-11-1-111iiii−i−i−i−iiiii−i−i−i−i−i−iii1-1−ii1-1
χ611111-1-11-11-1-1-1111-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii1-1−ii1-1-1-1-1-111-11-1111-1-1-111-11-1-111iiii−i−i−i−iiiii−i−i−i−iii−i−i-11i−i-11
χ621111-1-11-11-1-1-11-1-1111-1-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i1-1−ii-11-1-1-1-111-11-1111-111-1-1-1111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iii-11i−i1-1
χ631111-1-11-11-1-1-11-1-1111-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iii-11i−i1-1-1-1-1-111-11-1111-111-1-1-1111-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i1-1−ii-11
χ641111-1-11-11-1-1-11-1-1111-1-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i-11−ii1-1-1-1-1-111-11-1111-111-1-1-1111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iii1-1i−i-11
χ651111-1-11-11-1-1-11-1-1111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iii1-1i−i-11-1-1-1-111-11-1111-111-1-1-1111-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i-11−ii1-1
χ662222222222-2-2-22222-2-2-2-2-2-200000000000000000000000000-2-2-2-2-2-2-2-2-2-2222-2-2-2-222222200000000000000000000000000
χ672222222222-2-2-2-2-2-2-2-2-2222200000000000000000000000000-2-2-2-2-2-2-2-2-2-2222222222-2-2-2-200000000000000000000000000
χ68222222-2-2-2-22220000-2-200000000000022-2-222-2-20000000000-2-2-2-2-2-22222-2-2-2000022000000000000-2-222-2-2220000000000
χ69222222-2-2-2-22220000-2-2000000000000-2-222-2-2220000000000-2-2-2-2-2-22222-2-2-200002200000000000022-2-222-2-20000000000
χ70222222-2-2-2-2-2-2-200002200002i2i−2i−2i2i2i−2i−2i000000000000000000-2-2-2-2-2-222222220000-2-20000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ71222222-2-2-2-2-2-2-20000220000−2i−2i2i2i−2i−2i2i2i000000000000000000-2-2-2-2-2-222222220000-2-200002i2i−2i−2i2i2i−2i−2i000000000000000000
χ722222-2-22-22-222-222-2-2-22-2-22200000000000000000000000000-2-2-2-222-22-22-2-22-2-2222-222-2-200000000000000000000000000
χ732222-2-22-22-222-2-2-222-2222-2-200000000000000000000000000-2-2-2-222-22-22-2-2222-2-22-2-2-22200000000000000000000000000
χ742222-2-2-22-2222-200002-2000022-2-2-2-222000000000000000000-2-2-2-2222-22-2-2-220000-220000-2-22222-2-2000000000000000000
χ752222-2-2-22-2222-200002-20000-2-22222-2-2000000000000000000-2-2-2-2222-22-2-2-220000-22000022-2-2-2-222000000000000000000
χ762222-2-2-22-22-2-220000-220000000000002i2i−2i−2i−2i−2i2i2i0000000000-2-2-2-2222-22-222-200002-2000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ772222-2-2-22-22-2-220000-22000000000000−2i−2i2i2i2i2i−2i−2i0000000000-2-2-2-2222-22-222-200002-20000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ7822-2-22-222-2-20002-22-20000002−22−22−22−22−22−22−22−20000000000-2-222-22-2-222000-22-22000000−22−22−22−22−22−22−22−220000000000
χ7922-2-22-222-2-20002-22-2000000−22−22−22−22−22−22−22−220000000000-2-222-22-2-222000-22-220000002−22−22−22−22−22−22−22−20000000000
χ8022-2-22-222-2-2000-22-220000002−22−22−22−2−22−22−22−220000000000-2-222-22-2-2220002-22-2000000−22−22−22−222−22−22−22−20000000000
χ8122-2-22-222-2-2000-22-22000000−22−22−22−222−22−22−22−20000000000-2-222-22-2-2220002-22-20000002−22−22−22−2−22−22−22−220000000000
χ8222-2-22-2-2-2220000000002i−2i2i−2ii2−i2−i2i2i2−i2−i2i22−2−222−2−220000000000-2-222-2222-2-2000000000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i2−222−2−222−20000000000
χ8322-2-22-2-2-2220000000002i−2i2i−2i−i2i2i2−i2−i2i2i2−i2−222−2−222−20000000000-2-222-2222-2-2000000000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i22−2−222−2−220000000000
χ8422-2-22-2-2-222000000000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i2−222−2−222−20000000000-2-222-2222-2-20000000002i−2i2i−2i−i2i2i2−i2−i2i2i2−i22−2−222−2−220000000000
χ8522-2-22-2-2-222000000000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i22−2−222−2−220000000000-2-222-2222-2-20000000002i−2i2i−2ii2−i2−i2i2i2−i2−i2i2−222−2−222−20000000000
χ8622-2-2-222-2-220002-2-22000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000-2-2222-2-222-2000-222-2000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000
χ8722-2-2-222-2-220002-2-22000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000-2-2222-2-222-2000-222-2000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000
χ8822-2-2-222-2-22000-222-2000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000-2-2222-2-222-20002-2-22000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000
χ8922-2-2-222-2-22000-222-2000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000-2-2222-2-222-20002-2-22000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000
χ9022-2-2-22-222-20000000002i−2i−2i2i2−2−22−222−2−i2i2i2−i2i2−i2−i2i20000000000-2-2222-22-2-22000000000−2i2i2i−2i−222−22−2−22i2−i2−i2i2−i2i2i2−i20000000000
χ9122-2-2-22-222-20000000002i−2i−2i2i−222−22−2−22i2−i2−i2i2−i2i2i2−i20000000000-2-2222-22-2-22000000000−2i2i2i−2i2−2−22−222−2−i2i2i2−i2i2−i2−i2i20000000000
χ9222-2-2-22-222-2000000000−2i2i2i−2i2−2−22−222−2i2−i2−i2i2−i2i2i2−i20000000000-2-2222-22-2-220000000002i−2i−2i2i−222−22−2−22−i2i2i2−i2i2−i2−i2i20000000000
χ9322-2-2-22-222-2000000000−2i2i2i−2i−222−22−2−22−i2i2i2−i2i2−i2−i2i20000000000-2-2222-22-2-220000000002i−2i−2i2i2−2−22−222−2i2−i2−i2i2−i2i2i2−i20000000000
χ944-4-440000004i−4i0000000000000000000000000002ζ3−2ζ32ζ−2ζ000000-444-4000000−4i4i000000000000000000000000000−2ζ32ζ3−2ζ2ζ000000
χ954-4-440000004i−4i000000000000000000000000000−2ζ32ζ3−2ζ2ζ000000-444-4000000−4i4i0000000000000000000000000002ζ3−2ζ32ζ−2ζ000000
χ964-4-44000000−4i4i0000000000000000000000000002ζ−2ζ2ζ3−2ζ3000000-444-40000004i−4i000000000000000000000000000−2ζ2ζ−2ζ32ζ3000000
χ974-4-44000000−4i4i000000000000000000000000000−2ζ2ζ−2ζ32ζ3000000-444-40000004i−4i0000000000000000000000000002ζ−2ζ2ζ3−2ζ3000000
χ988-88-8000000000000000000000000000000000000000000000-88-88000000000000000000000000000000000000000000000

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