Finite Group Databasebeta

← Group #127721

Character table — Group #127721

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111222222222222224444444488888888888888881616161611112222222222222244444444888888888888888816161616
order122222444444448888448888888888888816161616161616168888222222444444448888448888888888888816161616161616168888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-1-1111-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-11111111-1-1-1111-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1
χ61111111-1-1-1111-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1111111111-1-1-1111-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111
χ71111111-1-1-1111-1-1-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1111111111-1-1-1111-1-1-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ81111111-1-1-1111-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-11111111-1-1-1111-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ91111-1-1-111-111-1-111111-111-1-1-1-1ii−i−iii−i−i11-1-111-1-1i−ii−i1111-1-1-111-111-1-111111-111-1-1-1-1ii−i−iii−i−i11-1-111-1-1i−ii−i
χ101111-1-1-111-111-1-111111-111-1-1-1-1ii−i−iii−i−i-1-111-1-111−ii−ii1111-1-1-111-111-1-111111-111-1-1-1-1ii−i−iii−i−i-1-111-1-111−ii−ii
χ111111-1-1-111-111-1-111111-111-1-1-1-1−i−iii−i−iii11-1-111-1-1−ii−ii1111-1-1-111-111-1-111111-111-1-1-1-1−i−iii−i−iii11-1-111-1-1−ii−ii
χ121111-1-1-111-111-1-111111-111-1-1-1-1−i−iii−i−iii-1-111-1-111i−ii−i1111-1-1-111-111-1-111111-111-1-1-1-1−i−iii−i−iii-1-111-1-111i−ii−i
χ131111-1-1-1-1-1111-11-1-1-1-1-1111-1-11111-1-1-1-111ii−i−i−i−iii−iii−i1111-1-1-1-1-1111-11-1-1-1-1-1111-1-11111-1-1-1-111ii−i−i−i−iii−iii−i
χ141111-1-1-1-1-1111-11-1-1-1-1-1111-1-11111-1-1-1-111−i−iiiii−i−ii−i−ii1111-1-1-1-1-1111-11-1-1-1-1-1111-1-11111-1-1-1-111−i−iiiii−i−ii−i−ii
χ151111-1-1-1-1-1111-11-1-1-1-1-1111-1-111-1-11111-1-1ii−i−i−i−iiii−i−ii1111-1-1-1-1-1111-11-1-1-1-1-1111-1-111-1-11111-1-1ii−i−i−i−iiii−i−ii
χ161111-1-1-1-1-1111-11-1-1-1-1-1111-1-111-1-11111-1-1−i−iiiii−i−i−iii−i1111-1-1-1-1-1111-11-1-1-1-1-1111-1-111-1-11111-1-1−i−iiiii−i−i−iii−i
χ1722222222222222-2-2-2-222-2-2-2-2-2-20000000000000000000022222222222222-2-2-2-222-2-2-2-2-2-200000000000000000000
χ182222222-2-2-2222-22222-2-2-2-2-2-222000000000000000000002222222-2-2-2222-22222-2-2-2-2-2-22200000000000000000000
χ19222222-2222-2-2-220000-2-200000000000000i2−i2i2−i2i2−i2i2−i20000222222-2222-2-2-220000-2-200000000000000i2−i2i2−i2i2−i2i2−i20000
χ20222222-2222-2-2-220000-2-200000000000000−i2i2−i2i2−i2i2−i2i20000222222-2222-2-2-220000-2-200000000000000−i2i2−i2i2−i2i2−i2i20000
χ21222222-2-2-2-2-2-2-2-2000022000000000000002−22−2−22−220000222222-2-2-2-2-2-2-2-2000022000000000000002−22−2−22−220000
χ22222222-2-2-2-2-2-2-2-200002200000000000000−22−222−22−20000222222-2-2-2-2-2-2-2-200002200000000000000−22−222−22−20000
χ232222-2-2222-2-2-22-20000-2200000000000000i2−i2−i2i2i2−i2−i2i200002222-2-2222-2-2-22-20000-2200000000000000i2−i2−i2i2i2−i2−i2i20000
χ242222-2-2222-2-2-22-20000-2200000000000000−i2i2i2−i2−i2i2i2−i200002222-2-2222-2-2-22-20000-2200000000000000−i2i2i2−i2−i2i2i2−i20000
χ252222-2-22-2-22-2-22200002-2000000000000002−2−22−222−200002222-2-22-2-22-2-22200002-2000000000000002−2−22−222−20000
χ262222-2-22-2-22-2-22200002-200000000000000−222−22−2−2200002222-2-22-2-22-2-22200002-200000000000000−222−22−2−220000
χ272222-2-2-222-222-2-2-2-2-2-22-2-2-22222000000000000000000002222-2-2-222-222-2-2-2-2-2-22-2-2-2222200000000000000000000
χ282222-2-2-2-2-2222-222222-22-2-222-2-2000000000000000000002222-2-2-2-2-2222-222222-22-2-222-2-200000000000000000000
χ2922-2-22-220002-2-2022-2-20000002-22−22−22−22−200000000000022-2-22-220002-2-2022-2-20000002-22−22−22−22−2000000000000
χ3022-2-22-220002-2-2022-2-20000002-2−22−22−22−2200000000000022-2-22-220002-2-2022-2-20000002-2−22−22−22−22000000000000
χ3122-2-22-220002-2-20-2-222000000-22i2−i2i2−i2−i2i2−i2i200000000000022-2-22-220002-2-20-2-222000000-22i2−i2i2−i2−i2i2−i2i2000000000000
χ3222-2-22-220002-2-20-2-222000000-22−i2i2−i2i2i2−i2i2−i200000000000022-2-22-220002-2-20-2-222000000-22−i2i2−i2i2i2−i2i2−i2000000000000
χ3322-2-2-22-20002-22022-2-2000000-22i2−i2−i2i2i2−i2−i2i200000000000022-2-2-22-20002-22022-2-2000000-22i2−i2−i2i2i2−i2−i2i2000000000000
χ3422-2-2-22-20002-22022-2-2000000-22−i2i2i2−i2−i2i2i2−i200000000000022-2-2-22-20002-22022-2-2000000-22−i2i2i2−i2−i2i2i2−i2000000000000
χ3522-2-2-22-20002-220-2-2220000002-22−2−22−222−200000000000022-2-2-22-20002-220-2-2220000002-22−2−22−222−2000000000000
χ3622-2-2-22-20002-220-2-2220000002-2−222−22−2−2200000000000022-2-2-22-20002-220-2-2220000002-2−222−22−2−22000000000000
χ3744-4-44-4-4000-44400000000000000000000000000000000044-4-44-4-4000-444000000000000000000000000000000000
χ3844-4-4-444000-44-400000000000000000000000000000000044-4-4-444000-44-4000000000000000000000000000000000
χ394-44-4000004000-422−2222−22000022−2200000000000000000000004-44-4000004000-422−2222−22000022−220000000000000000000000
χ404-44-4000004000-4−2222−22220000−222200000000000000000000004-44-4000004000-4−2222−22220000−22220000000000000000000000
χ414-44-400000-4000422−2222−220000−222200000000000000000000004-44-400000-4000422−2222−220000−22220000000000000000000000
χ424-44-400000-40004−2222−2222000022−2200000000000000000000004-44-400000-40004−2222−2222000022−220000000000000000000000
χ434-4-440004i−4i0000022−22−2222002i2−2i20000000000000000000000004-4-440004i−4i0000022−22−2222002i2−2i2000000000000000000000000
χ444-4-440004i−4i00000−222222−2200−2i22i20000000000000000000000004-4-440004i−4i00000−222222−2200−2i22i2000000000000000000000000
χ454-4-44000−4i4i0000022−22−222200−2i22i20000000000000000000000004-4-44000−4i4i0000022−22−222200−2i22i2000000000000000000000000
χ464-4-44000−4i4i00000−222222−22002i2−2i20000000000000000000000004-4-44000−4i4i00000−222222−22002i2−2i2000000000000000000000000
χ471111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ481111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ4911111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5011111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ511111111-1-1-1111-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-1-1-1-1-1-1111-1-1-11111111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-1-111
χ521111111-1-1-1111-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111-1-1-1-1-1-1-1111-1-1-11111111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1
χ531111111-1-1-1111-1-1-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1-1-1-1-1-1111-1-1-11111111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1
χ541111111-1-1-1111-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-1-1-1-1-1-1111-1-1-11111111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-1-111
χ551111-1-1-111-111-1-111111-111-1-1-1-1ii−i−iii−i−i11-1-111-1-1i−ii−i-1-1-1-1111-1-11-1-111-1-1-1-1-11-1-11111−i−iii−i−iii-1-111-1-111−ii−ii
χ561111-1-1-111-111-1-111111-111-1-1-1-1ii−i−iii−i−i-1-111-1-111−ii−ii-1-1-1-1111-1-11-1-111-1-1-1-1-11-1-11111−i−iii−i−iii11-1-111-1-1i−ii−i
χ571111-1-1-111-111-1-111111-111-1-1-1-1−i−iii−i−iii11-1-111-1-1−ii−ii-1-1-1-1111-1-11-1-111-1-1-1-1-11-1-11111ii−i−iii−i−i-1-111-1-111i−ii−i
χ581111-1-1-111-111-1-111111-111-1-1-1-1−i−iii−i−iii-1-111-1-111i−ii−i-1-1-1-1111-1-11-1-111-1-1-1-1-11-1-11111ii−i−iii−i−i11-1-111-1-1−ii−ii
χ591111-1-1-1-1-1111-11-1-1-1-1-1111-1-11111-1-1-1-111ii−i−i−i−iii−iii−i-1-1-1-111111-1-1-11-111111-1-1-111-1-1-1-11111-1-1−i−iiiii−i−ii−i−ii
χ601111-1-1-1-1-1111-11-1-1-1-1-1111-1-11111-1-1-1-111−i−iiiii−i−ii−i−ii-1-1-1-111111-1-1-11-111111-1-1-111-1-1-1-11111-1-1ii−i−i−i−iii−iii−i
χ611111-1-1-1-1-1111-11-1-1-1-1-1111-1-111-1-11111-1-1ii−i−i−i−iiii−i−ii-1-1-1-111111-1-1-11-111111-1-1-111-1-111-1-1-1-111−i−iiiii−i−i−iii−i
χ621111-1-1-1-1-1111-11-1-1-1-1-1111-1-111-1-11111-1-1−i−iiiii−i−i−iii−i-1-1-1-111111-1-1-11-111111-1-1-111-1-111-1-1-1-111ii−i−i−i−iiii−i−ii
χ6322222222222222-2-2-2-222-2-2-2-2-2-200000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-222222200000000000000000000
χ642222222-2-2-2222-22222-2-2-2-2-2-22200000000000000000000-2-2-2-2-2-2-2222-2-2-22-2-2-2-2222222-2-200000000000000000000
χ65222222-2222-2-2-220000-2-200000000000000i2−i2i2−i2i2−i2i2−i20000-2-2-2-2-2-22-2-2-2222-200002200000000000000−i2i2−i2i2−i2i2−i2i20000
χ66222222-2222-2-2-220000-2-200000000000000−i2i2−i2i2−i2i2−i2i20000-2-2-2-2-2-22-2-2-2222-200002200000000000000i2−i2i2−i2i2−i2i2−i20000
χ67222222-2-2-2-2-2-2-2-2000022000000000000002−22−2−22−220000-2-2-2-2-2-2222222220000-2-200000000000000−22−222−22−20000
χ68222222-2-2-2-2-2-2-2-200002200000000000000−22−222−22−20000-2-2-2-2-2-2222222220000-2-2000000000000002−22−2−22−220000
χ692222-2-2222-2-2-22-20000-2200000000000000i2−i2−i2i2i2−i2−i2i20000-2-2-2-222-2-2-2222-2200002-200000000000000−i2i2i2−i2−i2i2i2−i20000
χ702222-2-2222-2-2-22-20000-2200000000000000−i2i2i2−i2−i2i2i2−i20000-2-2-2-222-2-2-2222-2200002-200000000000000i2−i2−i2i2i2−i2−i2i20000
χ712222-2-22-2-22-2-22200002-2000000000000002−2−22−222−20000-2-2-2-222-222-222-2-20000-2200000000000000−222−22−2−220000
χ722222-2-22-2-22-2-22200002-200000000000000−222−22−2−220000-2-2-2-222-222-222-2-20000-22000000000000002−2−22−222−20000
χ732222-2-2-222-222-2-2-2-2-2-22-2-2-2222200000000000000000000-2-2-2-2222-2-22-2-2222222-2222-2-2-2-200000000000000000000
χ742222-2-2-2-2-2222-222222-22-2-222-2-200000000000000000000-2-2-2-222222-2-2-22-2-2-2-2-22-222-2-22200000000000000000000
χ7522-2-22-220002-2-2022-2-20000002-22−22−22−22−2000000000000-2-222-22-2000-2220-2-222000000-22−22−22−22−22000000000000
χ7622-2-22-220002-2-2022-2-20000002-2−22−22−22−22000000000000-2-222-22-2000-2220-2-222000000-222−22−22−22−2000000000000
χ7722-2-22-220002-2-20-2-222000000-22i2−i2i2−i2−i2i2−i2i2000000000000-2-222-22-2000-222022-2-20000002-2−i2i2−i2i2i2−i2i2−i2000000000000
χ7822-2-22-220002-2-20-2-222000000-22−i2i2−i2i2i2−i2i2−i2000000000000-2-222-22-2000-222022-2-20000002-2i2−i2i2−i2−i2i2−i2i2000000000000
χ7922-2-2-22-20002-22022-2-2000000-22i2−i2−i2i2i2−i2−i2i2000000000000-2-2222-22000-22-20-2-2220000002-2−i2i2i2−i2−i2i2i2−i2000000000000
χ8022-2-2-22-20002-22022-2-2000000-22−i2i2i2−i2−i2i2i2−i2000000000000-2-2222-22000-22-20-2-2220000002-2i2−i2−i2i2i2−i2−i2i2000000000000
χ8122-2-2-22-20002-220-2-2220000002-22−2−22−222−2000000000000-2-2222-22000-22-2022-2-2000000-22−222−22−2−22000000000000
χ8222-2-2-22-20002-220-2-2220000002-2−222−22−2−22000000000000-2-2222-22000-22-2022-2-2000000-222−2−22−222−2000000000000
χ8344-4-44-4-4000-444000000000000000000000000000000000-4-444-4440004-4-4000000000000000000000000000000000
χ8444-4-4-444000-44-4000000000000000000000000000000000-4-4444-4-40004-44000000000000000000000000000000000
χ854-44-4000004000-422−2222−22000022−220000000000000000000000-44-4400000-40004−2222−22220000−22220000000000000000000000
χ864-44-4000004000-4−2222−22220000−22220000000000000000000000-44-4400000-4000422−2222−22000022−220000000000000000000000
χ874-44-400000-4000422−2222−220000−22220000000000000000000000-44-44000004000-4−2222−2222000022−220000000000000000000000
χ884-44-400000-40004−2222−2222000022−220000000000000000000000-44-44000004000-422−2222−220000−22220000000000000000000000
χ894-4-440004i−4i0000022−22−2222002i2−2i2000000000000000000000000-444-4000−4i4i00000−222222−2200−2i22i2000000000000000000000000
χ904-4-440004i−4i00000−222222−2200−2i22i2000000000000000000000000-444-4000−4i4i0000022−22−2222002i2−2i2000000000000000000000000
χ914-4-44000−4i4i0000022−22−222200−2i22i2000000000000000000000000-444-40004i−4i00000−222222−22002i2−2i2000000000000000000000000
χ924-4-44000−4i4i00000−222222−22002i2−2i2000000000000000000000000-444-40004i−4i0000022−22−222200−2i22i2000000000000000000000000

Here i is the imaginary unit (i² = −1).