Finite Group Databasebeta

← Group #10705477

Character table — Group #10705477

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444444444448888888888888888888888888888888888242424242424242448484848
order122222344446661212121222444444661212121212121212121244668888888812121212121224242424242424242424242424242424444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1iiii−i−i−i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i11-1-1
χ6111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1iiii−i−i−i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111
χ7111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1−i−i−i−iiiii1111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-111
χ8111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1−i−i−i−iiiii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii11-1-1
χ91111111-1-1-1-1111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-11-1
χ101111111-1-1-1-1111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-11-11
χ111111111-1-1-1-1111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11-11
χ121111111-1-1-1-1111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111-11-1
χ131111111-1-1-1-1111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-11-1-1ii−i−i−i−iii11-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111111-1-1-1-1111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-11-1-1ii−i−i−i−iii11-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111111-1-1-1-1111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-11-1-1−i−iiiii−i−i11-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111111-1-1-1-1111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-11-1-1−i−iiiii−i−i11-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ172222222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22200000000-2-2-2-2220000000000000000000000000000
χ18222222222222222222-2-2-2-22222222222222222-2-2-2-200000000-2-2-2-2-2-20000000000000000000000000000
χ192222222-2-2-2-2222-2-2-2-222-2-222-2-222-2-22222-2-2-2-22-22200000000-2-222-2-20000000000000000000000000000
χ202222222-2-2-2-2222-2-2-2-2-2-222-2-22222-2-2-2-2-2-222222-2-2-200000000-2-222220000000000000000000000000000
χ21222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-11111111111111111000000000000
χ23222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-2-2-1-1000000001111-1-133−3−333−3−333−3−333−3−3000000000000
χ24222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-2-2-1-1000000001111-1-1−3−333−3−333−3−333−3−333000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-21100000000111111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-21100000000111111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111122112i2i2i2i−2i−2i−2i−2i-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111112211−2i−2i−2i−2i2i2i2i2i-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i000000000000
χ29222222-1-2-2-2-2-1-1-1111122-2-222-2-2-1-111-1-1-1-111112-2-1-10000000011-1-11133−3−3−3−33333−3−3−3−333000000000000
χ30222222-1-2-2-2-2-1-1-1111122-2-222-2-2-1-111-1-1-1-111112-2-1-10000000011-1-111−3−33333−3−3−3−33333−3−3000000000000
χ31222222-1-2-2-2-2-1-1-1111122-2-2-2-222-1-1111111-1-1-1-1-22-1-122-2-222-2-2-1-11111-1-1-1-11111-1-1-1-11111000000000000
χ32222222-1-2-2-2-2-1-1-1111122-2-2-2-222-1-1111111-1-1-1-1-22-1-1-2-222-2-222-1-111111111-1-1-1-11111-1-1-1-1000000000000
χ33222222-1-2-2-2-2-1-1-11111-2-22222-2-2-1-111-1-1-1-11111-22112i2i−2i−2i−2i−2i2i2i-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ34222222-1-2-2-2-2-1-1-11111-2-22222-2-2-1-111-1-1-1-11111-2211−2i−2i2i2i2i2i−2i−2i-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii000000000000
χ35222222-1-2-2-2-2-1-1-11111-2-222-2-222-1-1111111-1-1-1-12-2110000000011-1-1-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000000000000
χ36222222-1-2-2-2-2-1-1-11111-2-222-2-222-1-1111111-1-1-1-12-2110000000011-1-1-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3000000000000
χ3722-2-22-2222-2-22-2-222-2-22-22-200002-22-200000000002-22−22−22−22−200002-22−22−22−22−22−22−22−22−2000000000000
χ3822-2-22-2222-2-22-2-222-2-22-22-200002-22-200000000002-2−22−22−22−2200002-2−22−22−22−22−22−22−22−22000000000000
χ3922-2-22-2222-2-22-2-222-2-2-22-2200002-22-20000000000-22−i2i2−i2i2i2−i2i2−i20000-22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ4022-2-22-2222-2-22-2-222-2-2-22-2200002-22-20000000000-22i2−i2i2−i2−i2i2−i2i20000-22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ4122-2-22-22-2-2222-2-2-2-2222-2-2200002-2-2200000000002-22−2−222−2−220000-222−22−2−22−222−22−2−22−22000000000000
χ4222-2-22-22-2-2222-2-2-2-2222-2-2200002-2-2200000000002-2−222−2−222−20000-22−22−222−22−2−22−222−22−2000000000000
χ4322-2-22-22-2-2222-2-2-2-222-222-200002-2-220000000000-22−i2i2i2−i2i2−i2−i2i200002-2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ4422-2-22-22-2-2222-2-2-2-222-222-200002-2-220000000000-22i2−i2−i2i2−i2i2i2−i200002-2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ4522-2-22-2-122-2-2-111-1-1112-22-20000-11-1133−3−333−3−300-112−22−22−22−23−33−3-11ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ4622-2-22-2-122-2-2-111-1-1112-22-20000-11-1133−3−333−3−300-11−22−22−22−223−33−3-11−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ4722-2-22-2-122-2-2-111-1-1112-22-20000-11-11−3−333−3−33300-112−22−22−22−2−33−33-11ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ4822-2-22-2-122-2-2-111-1-1112-22-20000-11-11−3−333−3−33300-11−22−22−22−22−33−33-11−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ4922-2-22-2-122-2-2-111-1-111-22-220000-11-1133−3−333−3−3001-1−i2i2−i2i2i2−i2i2−i2−33−331-1ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ5022-2-22-2-122-2-2-111-1-111-22-220000-11-1133−3−333−3−3001-1i2−i2i2−i2−i2i2−i2i2−33−331-1−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ5122-2-22-2-122-2-2-111-1-111-22-220000-11-11−3−333−3−333001-1−i2i2−i2i2i2−i2i2−i23−33−31-1ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ5222-2-22-2-122-2-2-111-1-111-22-220000-11-11−3−333−3−333001-1i2−i2i2−i2−i2i2−i2i23−33−31-1−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ5322-2-22-2-1-2-222-11111-1-12-2-220000-111-133−3−3−3−33300-112−2−222−2−22−333−31-1ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ5422-2-22-2-1-2-222-11111-1-12-2-220000-111-133−3−3−3−33300-11−222−2−222−2−333−31-1−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ5522-2-22-2-1-2-222-11111-1-12-2-220000-111-1−3−33333−3−300-112−2−222−2−223−3−331-1ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ5622-2-22-2-1-2-222-11111-1-12-2-220000-111-1−3−33333−3−300-11−222−2−222−23−3−331-1−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ5722-2-22-2-1-2-222-11111-1-1-222-20000-111-133−3−3−3−333001-1−i2i2i2−i2i2−i2−i2i23−3−33-11ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ5822-2-22-2-1-2-222-11111-1-1-222-20000-111-133−3−3−3−333001-1i2−i2−i2i2−i2i2i2−i23−3−33-11−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ5922-2-22-2-1-2-222-11111-1-1-222-20000-111-1−3−33333−3−3001-1−i2i2i2−i2i2−i2−i2i2−333−3-11ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ6022-2-22-2-1-2-222-11111-1-1-222-20000-111-1−3−33333−3−3001-1i2−i2−i2i2−i2i2i2−i2−333−3-11−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ6122-2-2-2222-22-22-2-222-2-200002i−2i2i−2i-22-222i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ6222-2-2-2222-22-22-2-222-2-200002i−2i2i−2i-22-222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ6322-2-2-2222-22-22-2-222-2-20000−2i2i−2i2i-22-22−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ6422-2-2-2222-22-22-2-222-2-20000−2i2i−2i2i-22-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ6522-2-2-222-22-222-2-2-2-22200002i−2i−2i2i-222-22i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000
χ6622-2-2-222-22-222-2-2-2-22200002i−2i−2i2i-222-22i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000
χ6722-2-2-222-22-222-2-2-2-2220000−2i2i2i−2i-222-2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000
χ6822-2-2-222-22-222-2-2-2-2220000−2i2i2i−2i-222-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000
χ694444-4-444-4-44444444400000000-4-4-4-4000000000000000000000000000000000000000000000000000000
χ704444-4-44-444-4444-4-4-4-400000000-4-444000000000000000000000000000000000000000000000000000000
χ714444-4-4-24-4-44-2-2-2-2-2-2-2000000002222−2i32i32i3−2i3−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ724444-4-4-24-4-44-2-2-2-2-2-2-20000000022222i3−2i3−2i32i32i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ734444-4-4-2-444-4-2-2-222220000000022-2-2−2i32i32i3−2i32i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ744444-4-4-2-444-4-2-2-222220000000022-2-22i3−2i3−2i32i3−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ7544-4-4-44-24-44-4-222-2-22200004i−4i4i−4i2-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ7644-4-4-44-24-44-4-222-2-2220000−4i4i−4i4i2-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ7744-4-4-44-2-44-44-22222-2-200004i−4i−4i4i2-2-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ7844-4-4-44-2-44-44-22222-2-20000−4i4i4i−4i2-2-222i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ798-88-80080000-88-80000000000000000000000000000000000000000000000000000000000000000000000
χ808-88-800-400004-4443−4343−43000000000000000000000000000000000000000000000000000000000000000000
χ818-88-800-400004-44−4343−4343000000000000000000000000000000000000000000000000000000000000000000
χ828-8-880080000-8-880000000000000000000000000000000000000000000000000000000000000000000000
χ838-8-8800-4000044-443−43−4343000000000000000000000000000000000000000000000000000000000000000000
χ848-8-8800-4000044-4−434343−43000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.