Finite Group Databasebeta

← Group #10721

Character table — Group #10721

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size1111111111111111222222222222222222222222222222222222222222222222222222228888888888888888
order1222222222222222222222224444444444444444888888888888888888888888888888884444444444444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ91111111-1-1-1-11-1-1-1-11111-1-1-1-1111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111-1-1-1-11-1-1-1-11111-1-1-1-1111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111-1-1-1-11-1-1-1-11111-1-1-1-1111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iii−i−iii
χ121111111-1-1-1-11-1-1-1-11111-1-1-1-1111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−iii−i−i
χ131111111-1-1-1-11-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−iii
χ141111111-1-1-1-11-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iiiii−i−i
χ151111111-1-1-1-11-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111-1-1-1-11-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ17111-1-1-1-111-1-1111-1-111-1-111-1-111-111-1-111-1-111-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−ii−ii−i
χ18111-1-1-1-111-1-1111-1-111-1-111-1-111-111-1-111-1-111-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−ii−ii−ii
χ19111-1-1-1-111-1-1111-1-111-1-111-1-111-111-1-111-1-111-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii−ii−ii
χ20111-1-1-1-111-1-1111-1-111-1-111-1-111-111-1-111-1-111-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−ii−ii−i
χ21111-1-1-1-111-1-1111-1-1-1-111-1-11111-111-1-1-1-111-1-111-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1-11-1-11-11i−ii−i−ii−ii
χ22111-1-1-1-111-1-1111-1-1-1-111-1-11111-111-1-1-1-111-1-111-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-111-11-1−ii−iii−ii−i
χ23111-1-1-1-111-1-1111-1-1-1-111-1-11111-111-1-1-1-111-1-111-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1-11-1-11-11−ii−iii−ii−i
χ24111-1-1-1-111-1-1111-1-1-1-111-1-11111-111-1-1-1-111-1-111-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-111-11-1i−ii−i−ii−ii
χ25111-1-1-1-1-1-1111-1-11111-1-1-1-11111-1-1-11111-1-1-1-111-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiii−i−iii−i−ii-111-1-111-1
χ26111-1-1-1-1-1-1111-1-11111-1-1-1-11111-1-1-11111-1-1-1-111-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−iii−i−iii−i1-1-111-1-11
χ27111-1-1-1-1-1-1111-1-11111-1-1-1-11111-1-1-11111-1-1-1-111-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−ii−i−iii−i−ii1-1-111-1-11
χ28111-1-1-1-1-1-1111-1-11111-1-1-1-11111-1-1-11111-1-1-1-111-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−iii−i−iii−i-111-1-111-1
χ29111-1-1-1-1-1-1111-1-111-1-11111-1-111-1-1-111-1-11111-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−ii−i−ii−iii−i-111-11-1-11
χ30111-1-1-1-1-1-1111-1-111-1-11111-1-111-1-1-111-1-11111-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−iii−ii−i−ii1-1-11-111-1
χ31111-1-1-1-1-1-1111-1-111-1-11111-1-111-1-1-111-1-11111-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiii−i−ii−iii−i1-1-11-111-1
χ32111-1-1-1-1-1-1111-1-111-1-11111-1-111-1-1-111-1-11111-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−iii−ii−i−ii-111-11-1-11
χ33222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2000000000000000000000000000000000000000000000000
χ352222222-2-2-2-22-2-2-2-22222-2-2-2-2-2-2-22222-2-2-2-22222-2000000000000000000000000000000000000000000000000
χ362222222-2-2-2-22-2-2-2-2-2-2-2-22222-2-2-222222222-2-2-2-2-2000000000000000000000000000000000000000000000000
χ37222-2-2-2-222-2-2222-2-222-2-222-2-2-2-22-2-222-2-222-2-2222000000000000000000000000000000000000000000000000
χ38222-2-2-2-222-2-2222-2-2-2-222-2-222-2-22-2-22222-2-222-2-22000000000000000000000000000000000000000000000000
χ39222-2-2-2-2-2-2222-2-22222-2-2-2-222-2-2222-2-2-2-22222-2-22000000000000000000000000000000000000000000000000
χ40222-2-2-2-2-2-2222-2-222-2-22222-2-2-2-2222-2-222-2-2-2-2222000000000000000000000000000000000000000000000000
χ4122-222-2-22222-2-2-2-2-22-22-22-22-2000000000000000022−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−20000000000000000
χ4222-222-2-22222-2-2-2-2-22-22-22-22-20000000000000000−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−2220000000000000000
χ4322-222-2-22222-2-2-2-2-2-22-22-22-22000000000000000022−2−222−2−222−2−222−2−2−2−222−2−222−2−222−2−2220000000000000000
χ4422-222-2-22222-2-2-2-2-2-22-22-22-220000000000000000−2−222−2−222−2−222−2−22222−2−222−2−222−2−222−2−20000000000000000
χ4522-222-2-2-2-2-2-2-222222-22-2-22-22000000000000000022−2−222−2−2−2−222−2−22222−2−222−2−2−2−222−2−2220000000000000000
χ4622-222-2-2-2-2-2-2-222222-22-2-22-220000000000000000−2−222−2−22222−2−222−2−2−2−222−2−22222−2−222−2−20000000000000000
χ4722-222-2-2-2-2-2-2-22222-22-222-22-2000000000000000022−2−222−2−2−2−222−2−222−2−222−2−22222−2−222−2−20000000000000000
χ4822-222-2-2-2-2-2-2-22222-22-222-22-20000000000000000−2−222−2−22222−2−222−2−222−2−222−2−2−2−222−2−2220000000000000000
χ4922-2-2-22222-2-2-2-2-2222-2-222-2-220000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ5022-2-2-22222-2-2-2-2-2222-2-222-2-220000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ5122-2-2-22222-2-2-2-2-222-222-2-222-20000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ5222-2-2-22222-2-2-2-2-222-222-2-222-20000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ5322-2-2-222-2-222-222-2-22-2-22-222-20000000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ5422-2-2-222-2-222-222-2-22-2-22-222-20000000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ5522-2-2-222-2-222-222-2-2-222-22-2-220000000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ5622-2-2-222-2-222-222-2-2-222-22-2-220000000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ572-222-22-22-22-2-22-22-20000000000000002i−2i2i−2i2i−2i2i−2i0i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22−22−22−22−22−22−22−22−20000000000000000
χ582-222-22-22-22-2-22-22-20000000000000002i−2i2i−2i2i−2i2i−2i0−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−22−22−22−22−22−22−22−220000000000000000
χ592-222-22-22-22-2-22-22-2000000000000000−2i2i−2i2i−2i2i−2i2i0i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−22−22−22−22−22−22−22−220000000000000000
χ602-222-22-22-22-2-22-22-2000000000000000−2i2i−2i2i−2i2i−2i2i0−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22−22−22−22−22−22−22−22−20000000000000000
χ612-222-22-2-22-22-2-22-220000000000000002i−2i2i−2i−2i2i−2i2i0i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i22−22−22−22−2−22−22−22−220000000000000000
χ622-222-22-2-22-22-2-22-220000000000000002i−2i2i−2i−2i2i−2i2i0−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−22−22−22−222−22−22−22−20000000000000000
χ632-222-22-2-22-22-2-22-22000000000000000−2i2i−2i2i2i−2i2i−2i0i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−22−22−22−222−22−22−22−20000000000000000
χ642-222-22-2-22-22-2-22-22000000000000000−2i2i−2i2i2i−2i2i−2i0−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i22−22−22−22−2−22−22−22−220000000000000000
χ652-22-22-222-2-22-22-2-220000000000000002i−2i−2i2i2i−2i−2i2i02−22−2−22−222−22−2−22−22−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ662-22-22-222-2-22-22-2-220000000000000002i−2i−2i2i2i−2i−2i2i0−22−222−22−2−22−222−22−2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ672-22-22-222-2-22-22-2-22000000000000000−2i2i2i−2i−2i2i2i−2i02−22−2−22−222−22−2−22−22i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ682-22-22-222-2-22-22-2-22000000000000000−2i2i2i−2i−2i2i2i−2i0−22−222−22−2−22−222−22−2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ692-22-22-22-222-2-2-222-20000000000000002i−2i−2i2i−2i2i2i−2i02−22−2−22−22−22−222−22−2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ702-22-22-22-222-2-2-222-20000000000000002i−2i−2i2i−2i2i2i−2i0−22−222−22−22−22−2−22−22i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ712-22-22-22-222-2-2-222-2000000000000000−2i2i2i−2i2i−2i−2i2i02−22−2−22−22−22−222−22−2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ722-22-22-22-222-2-2-222-2000000000000000−2i2i2i−2i2i−2i−2i2i0−22−222−22−22−22−2−22−22−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ732-2-22-2-222-22-22-22-22000000002-222-22-200000000-22i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ742-2-22-2-222-22-22-22-22000000002-222-22-200000000-2−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ752-2-22-2-222-22-22-22-2200000000-22-2-22-2200000000200000000000000002-2-222-2-222-2-222-2-220000000000000000
χ762-2-22-2-222-22-22-22-2200000000-22-2-22-220000000020000000000000000-222-2-222-2-222-2-222-20000000000000000
χ772-2-22-2-22-22-2222-22-2000000002-22-22-2200000000-22i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ782-2-22-2-22-22-2222-22-2000000002-22-22-2200000000-2−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ792-2-22-2-22-22-2222-22-200000000-22-22-22-200000000200000000000000002-2-222-2-22-222-2-222-20000000000000000
χ802-2-22-2-22-22-2222-22-200000000-22-22-22-20000000020000000000000000-222-2-222-22-2-222-2-220000000000000000
χ812-2-2-222-22-2-222-222-2000000002-2-22-2-220000000022-2-22-222-22-2-22-222-200000000000000000000000000000000
χ822-2-2-222-22-2-222-222-2000000002-2-22-2-22000000002-222-22-2-22-222-22-2-2200000000000000000000000000000000
χ832-2-2-222-22-2-222-222-200000000-222-222-200000000-200000000000000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i0000000000000000
χ842-2-2-222-22-2-222-222-200000000-222-222-200000000-20000000000000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i0000000000000000
χ852-2-2-222-2-222-222-2-22000000002-2-2-222-20000000022-2-22-222-2-222-22-2-2200000000000000000000000000000000
χ862-2-2-222-2-222-222-2-22000000002-2-2-222-2000000002-222-22-2-222-2-22-222-200000000000000000000000000000000
χ872-2-2-222-2-222-222-2-2200000000-2222-2-2200000000-200000000000000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i0000000000000000
χ882-2-2-222-2-222-222-2-2200000000-2222-2-2200000000-20000000000000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i0000000000000000

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