Finite Group Databasebeta

← Group #10697008

Character table — Group #10697008

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444448888888888888888888888884848484848484848
order12222234444444466612121212121212121212121244668888888812121212121224242424242424242424242424242424888888882424242424242424242424242424242424444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111
χ922222222-2-222-2-22222-2-2-2-22222-2-2-2-2-2-2220000000022-2-2-2-20000000000000000000022-2-2000000002222-2-2-2-200000000
χ1022222222-2-222-2-22222-2-2-2-22222-2-2-2-2-2-2220000000022-2-2-2-200000000000000000000-2-22200000000-2-2-2-2222200000000
χ112222222-222-2-2-2-2-22222222-2-2-2-2-2-2-2-22-22200000000-2-222-2-200000000000000000000000000000000000000000000002i−2i
χ122222222-222-2-2-2-2-22222222-2-2-2-2-2-2-2-22-22200000000-2-222-2-20000000000000000000000000000000000000000000000−2i2i
χ132222222-2-2-2-2-222-2222-2-2-2-2-2-2-2-22222-222200000000-2-2-2-2220000000000000000000000000000000000000000002-20000
χ142222222-2-2-2-2-222-2222-2-2-2-2-2-2-2-22222-222200000000-2-2-2-222000000000000000000000000000000000000000000-220000
χ15222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ16222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000
χ17222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000
χ18222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000
χ19222222-12-2-222-2-22-1-1-11111-1-1-1-11111-2-2-1-100000000-1-1111133333333−3−3−3−3−3−3−3−3000022-2-23333−3−3−3−3-1-1-1-1111100000000
χ20222222-12-2-222-2-22-1-1-11111-1-1-1-11111-2-2-1-100000000-1-1111133333333−3−3−3−3−3−3−3−30000-2-222−3−3−3−333331111-1-1-1-100000000
χ21222222-12-2-222-2-22-1-1-11111-1-1-1-11111-2-2-1-100000000-1-11111−3−3−3−3−3−3−3−333333333000022-2-2−3−3−3−33333-1-1-1-1111100000000
χ22222222-12-2-222-2-22-1-1-11111-1-1-1-11111-2-2-1-100000000-1-11111−3−3−3−3−3−3−3−3333333330000-2-2223333−3−3−3−31111-1-1-1-100000000
χ232222-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-2-22-2-22222-2-2-2-222-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ242222-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-2-22-2-2-2-2-2-2222222-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ252222-2-222-2-2-2-2222222-2-2-2-2-2-2-2-222222-2-2-2000000002222-2-2000000000000000022-2-2000022-2-222-2-20000000000000000
χ262222-2-222-2-2-2-2222222-2-2-2-2-2-2-2-222222-2-2-2000000002222-2-20000000000000000-2-2220000-2-222-2-2220000000000000000
χ272222-2-22-2222222-2222222222222222-2-2-2-200000000-2-2-2-2-2-200000000000000000000000000000000000000002-2000000
χ282222-2-22-2222222-2222222222222222-2-2-2-200000000-2-2-2-2-2-20000000000000000000000000000000000000000-22000000
χ292222-2-22-2-2-222-2-2-2222-2-2-2-22222-2-2-2-222-2-200000000-2-22222000000000000000000000000000000000000000000002-200
χ302222-2-22-2-2-222-2-2-2222-2-2-2-22222-2-2-2-222-2-200000000-2-2222200000000000000000000000000000000000000000000-2200
χ312222-2-2-1222-2-2-2-22-1-1-1-1-1-1-111111111-22112222-2-2-2-2-1-111-1-1-1-1-1-11111-1-1-1-111110000000033−3−3−3−33333−3−333−3−300000000
χ322222-2-2-1222-2-2-2-22-1-1-1-1-1-1-111111111-22112222-2-2-2-2-1-111-1-1-1-1-1-11111-1-1-1-1111100000000−3−33333−3−3−3−333−3−33300000000
χ332222-2-2-1222-2-2-2-22-1-1-1-1-1-1-111111111-2211-2-2-2-22222-1-111-1-11111-1-1-1-11111-1-1-1-10000000033−3−3−3−333−3−333−3−33300000000
χ342222-2-2-1222-2-2-2-22-1-1-1-1-1-1-111111111-2211-2-2-2-22222-1-111-1-11111-1-1-1-11111-1-1-1-100000000−3−33333−3−333−3−333−3−300000000
χ352222-2-2-12-2-2-2-2222-1-1-111111111-1-1-1-12-21100000000-1-1-1-1113333−3−3−3−3−3−3−3−3333322-2-20000-1-111-1-111−3−33333−3−300000000
χ362222-2-2-12-2-2-2-2222-1-1-111111111-1-1-1-12-21100000000-1-1-1-1113333−3−3−3−3−3−3−3−33333-2-222000011-1-111-1-133−3−3−3−33300000000
χ372222-2-2-12-2-2-2-2222-1-1-111111111-1-1-1-12-21100000000-1-1-1-111−3−3−3−333333333−3−3−3−322-2-20000-1-111-1-11133−3−3−3−33300000000
χ382222-2-2-12-2-2-2-2222-1-1-111111111-1-1-1-12-21100000000-1-1-1-111−3−3−3−333333333−3−3−3−3-2-222000011-1-111-1-1−3−33333−3−300000000
χ3922-2-22-22-2002-20022-2-2000022-2-20000002-222−2−222−2−22-2000022−2−222−2−222−2−222−2−2−i2i2−i2i2002i−2i−i2i2−i2i2−i2i2−i2i200002i−2i2i−2i00000000
χ4022-2-22-22-2002-20022-2-2000022-2-20000002-222−2−222−2−22-2000022−2−222−2−222−2−222−2−2i2−i2i2−i200−2i2ii2−i2i2−i2i2−i2i2−i20000−2i2i−2i2i00000000
χ4122-2-22-22-2002-20022-2-2000022-2-20000002-2−2−222−2−2222-20000−2−222−2−222−2−222−2−222−i2i2−i2i200−2i2i−i2i2−i2i2−i2i2−i2i20000−2i2i−2i2i00000000
χ4222-2-22-22-2002-20022-2-2000022-2-20000002-2−2−222−2−2222-20000−2−222−2−222−2−222−2−222i2−i2i2−i2002i−2ii2−i2i2−i2i2−i2i2−i200002i−2i2i−2i00000000
χ4322-2-22-2-1-2002-2002-11133−3−3-1-11133−3−300-1122−2−222−2−2-113−33−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−i2i2−i2i2002i−2iζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−i3i3−i3i3−ii−ii00000000
χ4422-2-22-2-1-2002-2002-11133−3−3-1-11133−3−300-1122−2−222−2−2-113−33−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23i2−i2i2−i200−2i2i−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23i3−i3i3−i3i−ii−i00000000
χ4522-2-22-2-1-2002-2002-11133−3−3-1-11133−3−300-11−2−222−2−222-113−33−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−i2i2−i2i200−2i2iζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23i3−i3i3−i3i−ii−i00000000
χ4622-2-22-2-1-2002-2002-11133−3−3-1-11133−3−300-11−2−222−2−222-113−33−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23i2−i2i2−i2002i−2i−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−i3i3−i3i3−ii−ii00000000
χ4722-2-22-2-1-2002-2002-111−3−333-1-111−3−33300-1122−2−222−2−2-11−33−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−i2i2−i2i2002i−2iζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7i3−i3i3−i3−ii−ii00000000
χ4822-2-22-2-1-2002-2002-111−3−333-1-111−3−33300-1122−2−222−2−2-11−33−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7i2−i2i2−i200−2i2i−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−i3i3−i3i3i−ii−i00000000
χ4922-2-22-2-1-2002-2002-111−3−333-1-111−3−33300-11−2−222−2−222-11−33−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−i2i2−i2i200−2i2iζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−i3i3−i3i3i−ii−i00000000
χ5022-2-22-2-1-2002-2002-111−3−333-1-111−3−33300-11−2−222−2−222-11−33−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7i2−i2i2−i2002i−2i−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7i3−i3i3−i3−ii−ii00000000
χ5122-2-2-222-200-220022-2-20000-2-222000000-2222−2−2−2−2222-2000022−2−2−2−22222−2−2−2−222−i2i2i2−i22i−2i00−i2i2i2−i2−i2i2i2−i22i−2i−2i2i000000000000
χ5222-2-2-222-200-220022-2-20000-2-222000000-2222−2−2−2−2222-2000022−2−2−2−22222−2−2−2−222i2−i2−i2i2−2i2i00i2−i2−i2i2i2−i2−i2i2−2i2i2i−2i000000000000
χ5322-2-2-222-200-220022-2-20000-2-222000000-22−2−22222−2−22-20000−2−22222−2−2−2−22222−2−2−i2i2i2−i2−2i2i00−i2i2i2−i2−i2i2i2−i2−2i2i2i−2i000000000000
χ5422-2-2-222-200-220022-2-20000-2-222000000-22−2−22222−2−22-20000−2−22222−2−2−2−22222−2−2i2−i2−i2i22i−2i00i2−i2−i2i2i2−i2−i2i22i−2i−2i2i000000000000
χ5522-2-2-22-1-200-22002-11133−3−311-1-1−3−333001-122−2−2−2−222-11−333−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−i2i2i2−i22i−2i00ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−iii−ii3−i3−i3i300000000
χ5622-2-2-22-1-200-22002-11133−3−311-1-1−3−333001-122−2−2−2−222-11−333−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23i2−i2−i2i2−2i2i00−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7i−i−ii−i3i3i3−i300000000
χ5722-2-2-22-1-200-22002-11133−3−311-1-1−3−333001-1−2−22222−2−2-11−333−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−i2i2i2−i2−2i2i00ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7i−i−ii−i3i3i3−i300000000
χ5822-2-2-22-1-200-22002-11133−3−311-1-1−3−333001-1−2−22222−2−2-11−333−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23i2−i2−i2i22i−2i00−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−iii−ii3−i3−i3i300000000
χ5922-2-2-22-1-200-22002-111−3−33311-1-133−3−3001-122−2−2−2−222-113−3−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−i2i2i2−i22i−2i00ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−iii−i−i3i3i3−i300000000
χ6022-2-2-22-1-200-22002-111−3−33311-1-133−3−3001-122−2−2−2−222-113−3−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7i2−i2−i2i2−2i2i00−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23i−i−iii3−i3−i3i300000000
χ6122-2-2-22-1-200-22002-111−3−33311-1-133−3−3001-1−2−22222−2−2-113−3−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−i2i2i2−i2−2i2i00ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23i−i−iii3−i3−i3i300000000
χ6222-2-2-22-1-200-22002-111−3−33311-1-133−3−3001-1−2−22222−2−2-113−3−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7i2−i2−i2i22i−2i00−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−iii−i−i3i3i3−i300000000
χ63444444-2-444-4-4-4-4-4-2-2-2-2-2-2-2222222224-4-2-20000000022-2-222000000000000000000000000000000000000000000000000
χ64444444-2-4-4-4-4-444-4-2-2-222222222-2-2-2-2-44-2-2000000002222-2-2000000000000000000000000000000000000000000000000
χ654444-4-4-2-4444444-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-4-42200000000222222000000000000000000000000000000000000000000000000
χ664444-4-4-2-4-4-444-4-4-4-2-2-22222-2-2-2-2222244220000000022-2-2-2-2000000000000000000000000000000000000000000000000
χ6744-4-44-44400-4400-44-4-40000-4-4440000004-400000000-440000000000000000000000000000000000000000000000000000
χ6844-4-44-4-2400-4400-4-2222323−23−2322-2-2−23−23232300-22000000002-223−23−2323000000000000000000000000000000000000000000000000
χ6944-4-44-4-2400-4400-4-222−23−23232322-2-22323−23−2300-22000000002-2−232323−23000000000000000000000000000000000000000000000000
χ7044-4-4-4444004-400-44-4-4000044-4-4000000-4400000000-440000000000000000000000000000000000000000000000000000
χ7144-4-4-44-24004-400-4-2222323−23−23-2-2222323−23−23002-2000000002-2−2323−2323000000000000000000000000000000000000000000000000
χ7244-4-4-44-24004-400-4-222−23−232323-2-222−23−232323002-2000000002-223−2323−23000000000000000000000000000000000000000000000000
χ734-44-4004000004-40-44-4000000004-44-400002i−2i2i−2i2i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.