Finite Group Databasebeta

← Group #10698709

Character table — Group #10698709

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order12222222344444444666666612121212121212124488888888121212121212121224242424242424242424242424242424224466668888121212122424242424242424444488884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111111-1-1
χ9222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000022-2-222220000-2-2-2-200000000000000000000
χ10222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000000000-2-222-2-2-2-20000222200000000000000000000
χ11222222222-2-2-22222-2222222222222222-2-200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000022-2-200000000
χ12222222222-2-2-22222-2222222222222222-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-22200000000
χ13222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-2-2-222220000000000000000000000000000000000000000000000002-200
χ14222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-2-2-22222000000000000000000000000000000000000000000000000-2200
χ1522222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ1622222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2111111111111000000000000
χ1722222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-1-1-1-1-2-2-2-2-1-1-1-111111111000000000000
χ1822222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2111122221111-1-1-1-1-1-1-1-1000000000000
χ1922222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-1111133333333−3−3−3−3−3−3−3−322-2-2-1-1-1-1000011113333−3−3−3−3000000000000
χ2022222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-1111133333333−3−3−3−3−3−3−3−3-2-22211110000-1-1-1-1−3−3−3−33333000000000000
χ2122222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-11111−3−3−3−3−3−3−3−33333333322-2-2-1-1-1-100001111−3−3−3−33333000000000000
χ2222222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-11111−3−3−3−3−3−3−3−333333333-2-22211110000-1-1-1-13333−3−3−3−3000000000000
χ23222-2-22-2-220002-2-22022-2-2-2-2222-2-2-2-222002222−2−2−2−2000000002222−2−2−2−22222−2−2−2−20000000000000000000000002i−2i00−i2−i2i2i20000
χ24222-2-22-2-220002-2-22022-2-2-2-2222-2-2-2-222002222−2−2−2−2000000002222−2−2−2−22222−2−2−2−2000000000000000000000000−2i2i00i2i2−i2−i20000
χ25222-2-22-2-220002-2-22022-2-2-2-2222-2-2-2-22200−2−2−2−2222200000000−2−2−2−22222−2−2−2−222220000000000000000000000002i−2i00i2i2−i2−i20000
χ26222-2-22-2-220002-2-22022-2-2-2-2222-2-2-2-22200−2−2−2−2222200000000−2−2−2−22222−2−2−2−22222000000000000000000000000−2i2i00−i2−i2i2i20000
χ2722-22-2-22-222-2-2000022-22-22-2-20000000000−i2−i2i2i2−i2−i2i2i222-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002i−2i000022−2−22i2i−2i−2i22−2−222−2−2000000000000
χ2822-22-2-22-222-2-2000022-22-22-2-20000000000−i2−i2i2i2−i2−i2i2i222-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200−2i2i0000−2−222−2i−2i2i2i−2−222−2−222000000000000
χ2922-22-2-22-222-2-2000022-22-22-2-20000000000i2i2−i2−i2i2i2−i2−i222-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002i−2i0000−2−2222i2i−2i−2i−2−222−2−222000000000000
χ3022-22-2-22-222-2-2000022-22-22-2-20000000000i2i2−i2−i2i2i2−i2−i222-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200−2i2i000022−2−2−2i−2i2i2i22−2−222−2−2000000000000
χ3122-22-2-22-2-12-2-200002-11-11-1113−333−3−33−300−i2−i2i2i2−i2−i2i2i2-1-1113−33−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23002i−2i−i3−i3i3i322−2−2−i−iiiζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ3222-22-2-22-2-12-2-200002-11-11-1113−333−3−33−300−i2−i2i2i2−i2−i2i2i2-1-1113−33−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300−2i2ii3i3−i3−i3−2−222ii−i−i−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ3322-22-2-22-2-12-2-200002-11-11-1113−333−3−33−300i2i2−i2−i2i2i2−i2−i2-1-1113−33−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23002i−2i−i3−i3i3i3−2−222−i−iii−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ3422-22-2-22-2-12-2-200002-11-11-1113−333−3−33−300i2i2−i2−i2i2i2−i2−i2-1-1113−33−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300−2i2ii3i3−i3−i322−2−2ii−i−iζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ3522-22-2-22-2-12-2-200002-11-11-111−33−3−333−3300−i2−i2i2i2−i2−i2i2i2-1-111−33−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7002i−2ii3i3−i3−i322−2−2−i−iiiζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ3622-22-2-22-2-12-2-200002-11-11-111−33−3−333−3300−i2−i2i2i2−i2−i2i2i2-1-111−33−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700−2i2i−i3−i3i3i3−2−222ii−i−i−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ3722-22-2-22-2-12-2-200002-11-11-111−33−3−333−3300i2i2−i2−i2i2i2−i2−i2-1-111−33−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7002i−2ii3i3−i3−i3−2−222−i−iii−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ3822-22-2-22-2-12-2-200002-11-11-111−33−3−333−3300i2i2−i2−i2i2i2−i2−i2-1-111−33−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700−2i2i−i3−i3i3i322−2−2ii−i−iζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ392-222-2-2-222-22-200002-22-222-2-20000000000−i2i2−i2i2−i2i2−i2i22-22-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22-2002-22-2−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2000000000000
χ402-222-2-2-222-22-200002-22-222-2-20000000000−i2i2−i2i2−i2i2−i2i22-22-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2-2200-22-22i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2000000000000
χ412-222-2-2-222-22-200002-22-222-2-20000000000i2−i2i2−i2i2−i2i2−i22-22-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22-2002-22-2i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2000000000000
χ422-222-2-2-222-22-200002-22-222-2-20000000000i2−i2i2−i2i2−i2i2−i22-22-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2-2200-22-22−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2000000000000
χ432-222-2-2-22-1-22-2000021-11-1-1113−33−33−3−3300−i2i2−i2i2−i2i2−i2i2-11-113−3−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ72-200-11-11−i2i2−i2i23−33−3ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ442-222-2-2-22-1-22-2000021-11-1-1113−33−33−3−3300−i2i2−i2i2−i2i2−i2i2-11-113−3−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7-22001-11-1i2−i2i2−i2−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ452-222-2-2-22-1-22-2000021-11-1-1113−33−33−3−3300i2−i2i2−i2i2−i2i2−i2-11-113−3−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ72-200-11-11i2−i2i2−i23−33−3−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ462-222-2-2-22-1-22-2000021-11-1-1113−33−33−3−3300i2−i2i2−i2i2−i2i2−i2-11-113−3−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7-22001-11-1−i2i2−i2i2−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ472-222-2-2-22-1-22-2000021-11-1-111−33−33−333−300−i2i2−i2i2−i2i2−i2i2-11-11−333−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ232-200-11-11−i2i2−i2i2−33−33ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ482-222-2-2-22-1-22-2000021-11-1-111−33−33−333−300−i2i2−i2i2−i2i2−i2i2-11-11−333−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23-22001-11-1i2−i2i2−i23−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ492-222-2-2-22-1-22-2000021-11-1-111−33−33−333−300i2−i2i2−i2i2−i2i2−i2-11-11−333−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ232-200-11-11i2−i2i2−i2−33−33−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ502-222-2-2-22-1-22-2000021-11-1-111−33−33−333−300i2−i2i2−i2i2−i2i2−i2-11-11−333−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23-22001-11-1−i2i2−i2i23−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ512-2-2222-2-2222-222-2-2-2-2-2-2-2222222-2-22-2-2-2200000000-222-2-2-222000000000000000000000000000000000000000000000000002i−2i
χ522-2-2222-2-2222-222-2-2-2-2-2-2-2222222-2-22-2-2-2200000000-222-2-2-22200000000000000000000000000000000000000000000000000−2i2i
χ532-2-2222-2-2222-2-2-222-2-2-2-2-2222-2-2-222-2222-200000000-222-222-2-2000000000000000000000000000000000000000000002i−2i2i−2i0000
χ542-2-2222-2-2222-2-2-222-2-2-2-2-2222-2-2-222-2222-200000000-222-222-2-200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ552-2-2222-2-22-2-2222-2-22-2-2-2-2222222-2-22-2-22-2000000002-2-2222-2-20000000000000000000000002i−2i−2i2i00002i−2i−2i2i2i−2i−2i2i000000000000
χ562-2-2222-2-22-2-2222-2-22-2-2-2-2222222-2-22-2-22-2000000002-2-2222-2-2000000000000000000000000−2i2i2i−2i0000−2i2i2i−2i−2i2i2i−2i000000000000
χ572-2-2222-2-22-2-22-2-2222-2-2-2-2222-2-2-222-222-222-2-222-2-222-2-22-2-2222-2-222-2-222-2-222-2-22000000000000000000000000000000000000
χ582-2-2222-2-22-2-22-2-2222-2-2-2-2222-2-2-222-222-22-222-2-222-22-2-22-2-222-222-2-222-2-222-2-222-2000000000000000000000000000000000000
χ592-2-2222-2-2-1-2-2222-2-221111-1-1-1-1-1-111-1112-200000000-111-1-1-1113−3−333−3−33−333−3−333−30000−i3i3i3−i3−2i2i2i−2i−i3i3i3−i3i−i−iii−i−ii000000000000
χ602-2-2222-2-2-1-2-2222-2-221111-1-1-1-1-1-111-1112-200000000-111-1-1-1113−3−333−3−33−333−3−333−30000i3−i3−i3i32i−2i−2i2ii3−i3−i3i3−iii−i−iii−i000000000000
χ612-2-2222-2-2-1-2-2222-2-221111-1-1-1-1-1-111-1112-200000000-111-1-1-111−333−3−333−33−3−333−3−330000−i3i3i3−i32i−2i−2i2i−i3i3i3−i3−iii−i−iii−i000000000000
χ622-2-2222-2-2-1-2-2222-2-221111-1-1-1-1-1-111-1112-200000000-111-1-1-111−333−3−333−33−3−333−3−330000i3−i3−i3i3−2i2i2i−2ii3−i3−i3i3i−i−iii−i−ii000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.