Finite Group Databasebeta

← Group #10697677

Character table — Group #10697677

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444448888888888888888888888884848484848484848
order122222344444444666666612121212121212124488888888121212121212121224242424242424242424242424242424444488881212121212121212242424242424242424448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-1-111
χ611111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1111-1-1
χ711111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ922222222-2-2222-2-2222222222222222-2-200000000-2-2-2-2-2-2-2-20000000000000000000022-2-2000000002222-2-2-2-200000000
χ1022222222-2-2222-2-2222222222222222-2-200000000-2-2-2-2-2-2-2-200000000000000000000-2-22200000000-2-2-2-2222200000000
χ112222222-222-2-2-2222222222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000022-2-200002222-2-2-2-20000000000000000
χ122222222-222-2-2-2222222222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000000000-2-2220000-2-2-2-222220000000000000000
χ132222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2222i2i2i2i−2i−2i−2i−2i-2-2-2-222222i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i00000000000000000000000000000000
χ142222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-222−2i−2i−2i−2i2i2i2i2i-2-2-2-22222−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i00000000000000000000000000000000
χ15222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ16222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000
χ17222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000
χ18222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000
χ19222222-12-2-2222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000011111111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3000022-2-2−i3−i3i3i3−i3−i3i3i3-1-1-1-1111100000000
χ20222222-12-2-2222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000011111111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i30000-2-222i3i3−i3−i3i3i3−i3−i31111-1-1-1-100000000
χ21222222-12-2-2222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000011111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3000022-2-2i3i3−i3−i3i3i3−i3−i3-1-1-1-1111100000000
χ22222222-12-2-2222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000011111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i30000-2-222−i3−i3i3i3−i3−i3i3i31111-1-1-1-100000000
χ23222222-1-222-2-2-222-1-1-1-1-1-1-111111111-2-200000000-1-1-1-111113333−3−3−3−3−3−3−3−3333322-2-20000-1-1-1-1111133−3−333−3−300000000
χ24222222-1-222-2-2-222-1-1-1-1-1-1-111111111-2-200000000-1-1-1-111113333−3−3−3−3−3−3−3−33333-2-22200001111-1-1-1-1−3−333−3−33300000000
χ25222222-1-222-2-2-222-1-1-1-1-1-1-111111111-2-200000000-1-1-1-11111−3−3−3−333333333−3−3−3−322-2-20000-1-1-1-11111−3−333−3−33300000000
χ26222222-1-222-2-2-222-1-1-1-1-1-1-111111111-2-200000000-1-1-1-11111−3−3−3−333333333−3−3−3−3-2-22200001111-1-1-1-133−3−333−3−300000000
χ27222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111222i2i2i2i−2i−2i−2i−2i1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii00000000−i3−i3i3i3i3i3−i3−i333−3−3−3−33300000000
χ28222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111222i2i2i2i−2i−2i−2i−2i1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii00000000i3i3−i3−i3−i3−i3i3i3−3−33333−3−300000000
χ29222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122−2i−2i−2i−2i2i2i2i2i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i00000000−i3−i3i3i3i3i3−i3−i3−3−33333−3−300000000
χ30222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122−2i−2i−2i−2i2i2i2i2i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i00000000i3i3−i3−i3−i3−i3i3i333−3−3−3−33300000000
χ312222-2-2222-2-2-222-2-2-2-2-222222-2-2-2-2222-20000000022-2-222-2-20000000000000000000000000000000000000000020-20000
χ322222-2-2222-2-2-222-2-2-2-2-222222-2-2-2-2222-20000000022-2-222-2-200000000000000000000000000000000000000000-2020000
χ332222-2-222-22-2-22-22-2-2-2-222222-2-2-2-222-2200000000-2-222-2-222000000000000000000000000000000000000000020-200000
χ342222-2-222-22-2-22-22-2-2-2-222222-2-2-2-222-2200000000-2-222-2-2220000000000000000000000000000000000000000-20200000
χ352222-2-22-22-222-22-2-2-2-2-2222-2-22222-2-2-220000000022-2-2-2-222000000000000000000000000000000000000000000002-200
χ362222-2-22-22-222-22-2-2-2-2-2222-2-22222-2-2-220000000022-2-2-2-22200000000000000000000000000000000000000000000-2200
χ372222-2-22-2-2222-2-22-2-2-2-2222-2-22222-2-22-200000000-2-22222-2-200000000000000000000000000000000000000000000002-2
χ382222-2-22-2-2222-2-22-2-2-2-2222-2-22222-2-22-200000000-2-22222-2-20000000000000000000000000000000000000000000000-22
χ392-22-22-2202-2000-2222-2-2-22-20000000000−i2−i2i2i2−i2−i2i2i22-22-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002-2−i2i2−i2i200002-22-2−i2i2−i2i2−i2i2−i2i200000000
χ402-22-22-2202-2000-2222-2-2-22-20000000000−i2−i2i2i2−i2−i2i2i22-22-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200-22i2−i2i2−i20000-22-22i2−i2i2−i2i2−i2i2−i200000000
χ412-22-22-2202-2000-2222-2-2-22-20000000000i2i2−i2−i2i2i2−i2−i22-22-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002-2i2−i2i2−i200002-22-2i2−i2i2−i2i2−i2i2−i200000000
χ422-22-22-2202-2000-2222-2-2-22-20000000000i2i2−i2−i2i2i2−i2−i22-22-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200-22−i2i2−i2i20000-22-22−i2i2−i2i2−i2i2−i2i200000000
χ432-22-22-220-220002-222-2-2-22-2000000000022−2−2−2−222-22-22000022−2−222−2−2−2−222−2−2222i−2i00−i2i2i2−i22i−2i2i−2i0000−i2i2−i2i2i2−i2i2−i200000000
χ442-22-22-220-220002-222-2-2-22-2000000000022−2−2−2−222-22-22000022−2−222−2−2−2−222−2−222−2i2i00i2−i2−i2i2−2i2i−2i2i0000i2−i2i2−i2−i2i2−i2i200000000
χ452-22-22-220-220002-222-2-2-22-20000000000−2−22222−2−2-22-220000−2−222−2−22222−2−222−2−22i−2i00i2−i2−i2i22i−2i2i−2i0000i2−i2i2−i2−i2i2−i2i200000000
χ462-22-22-220-220002-222-2-2-22-20000000000−2−22222−2−2-22-220000−2−222−2−22222−2−222−2−2−2i2i00−i2i2i2−i2−2i2i−2i2i0000−i2i2−i2i2i2−i2i2−i200000000
χ472-22-22-2-102-2000-22-1-1111-113−333−3−33−300−i2−i2i2i2−i2−i2i2i2-11-113−33−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7002-2−i2i2−i2i2−333−3-11-11ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ482-22-22-2-102-2000-22-1-1111-113−333−3−33−300−i2−i2i2i2−i2−i2i2i2-11-113−33−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700-22i2−i2i2−i23−3−331-11-1−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ492-22-22-2-102-2000-22-1-1111-113−333−3−33−300i2i2−i2−i2i2i2−i2−i2-11-113−33−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7002-2i2−i2i2−i2−333−3-11-11−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ502-22-22-2-102-2000-22-1-1111-113−333−3−33−300i2i2−i2−i2i2i2−i2−i2-11-113−33−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700-22−i2i2−i2i23−3−331-11-1ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ512-22-22-2-102-2000-22-1-1111-11−33−3−333−3300−i2−i2i2i2−i2−i2i2i2-11-11−33−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23002-2−i2i2−i2i23−3−33-11-11ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ522-22-22-2-102-2000-22-1-1111-11−33−3−333−3300−i2−i2i2i2−i2−i2i2i2-11-11−33−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300-22i2−i2i2−i2−333−31-11-1−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ532-22-22-2-102-2000-22-1-1111-11−33−3−333−3300i2i2−i2−i2i2i2−i2−i2-11-11−33−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23002-2i2−i2i2−i23−3−33-11-11−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ542-22-22-2-102-2000-22-1-1111-11−33−3−333−3300i2i2−i2−i2i2i2−i2−i2-11-11−33−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300-22−i2i2−i2i2−333−31-11-1ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ552-22-22-2-10-220002-2-1-1111-113−333−3−33−30022−2−2−2−2221-11-1−33−33ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ72i−2i00−i2i2i2−i2−ii−iii3−i3−i3i3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ562-22-22-2-10-220002-2-1-1111-113−333−3−33−30022−2−2−2−2221-11-1−33−33ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−2i2i00i2−i2−i2i2i−ii−i−i3i3i3−i3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ572-22-22-2-10-220002-2-1-1111-113−333−3−33−300−2−22222−2−21-11-1−33−33−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ72i−2i00i2−i2−i2i2−ii−iii3−i3−i3i3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ582-22-22-2-10-220002-2-1-1111-113−333−3−33−300−2−22222−2−21-11-1−33−33−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−2i2i00−i2i2i2−i2i−ii−i−i3i3i3−i3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ592-22-22-2-10-220002-2-1-1111-11−33−3−333−330022−2−2−2−2221-11-13−33−3ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ232i−2i00−i2i2i2−i2−ii−ii−i3i3i3−i3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ602-22-22-2-10-220002-2-1-1111-11−33−3−333−330022−2−2−2−2221-11-13−33−3ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−2i2i00i2−i2−i2i2i−ii−ii3−i3−i3i3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ612-22-22-2-10-220002-2-1-1111-11−33−3−333−3300−2−22222−2−21-11-13−33−3−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ232i−2i00i2−i2−i2i2−ii−ii−i3i3i3−i3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ622-22-22-2-10-220002-2-1-1111-11−33−3−333−3300−2−22222−2−21-11-13−33−3−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−2i2i00−i2i2i2−i2i−ii−ii3−i3−i3i3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ634444-4-4-244-4-4-444-42222-2-2-2-2-22222-2-24-400000000-2-222-2-222000000000000000000000000000000000000000000000000
χ644444-4-4-24-44-4-44-442222-2-2-2-2-22222-2-2-440000000022-2-222-2-2000000000000000000000000000000000000000000000000
χ654444-4-4-2-44-444-44-42222-2-2-222-2-2-2-222-4400000000-2-22222-2-2000000000000000000000000000000000000000000000000
χ664444-4-4-2-4-4444-4-442222-2-2-222-2-2-2-2224-40000000022-2-2-2-222000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.