Finite Group Databasebeta

← Group #10698908

Character table — Group #10698908

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444448888888888888888888888884848484848484848
order122222344444444666666612121212121212124488888888121212121212121224242424242424242424242424242424444488881212121212121212242424242424242444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ922222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000022-2-200002222-2-2-2-20000000000000000
χ1022222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000000000-2-2220000-2-2-2-222220000000000000000
χ112222222-22222-2-2-2222222222222222-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000002i−2i0000
χ122222222-22222-2-2-2222222222222222-2-200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000−2i2i0000
χ132222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-2-2-2222200000000000000000000000000000000000000000000002i−2i
χ142222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-2-2-222220000000000000000000000000000000000000000000000−2i2i
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
χ19222222-12-2-2-2-2222-1-1-1-1-1-1-111111111-2-200000000-1-1-1-1111133333333−3−3−3−3−3−3−3−322-2-20000-1-1-1-111113333−3−3−3−300000000
χ20222222-12-2-2-2-2222-1-1-1-1-1-1-111111111-2-200000000-1-1-1-1111133333333−3−3−3−3−3−3−3−3-2-22200001111-1-1-1-1−3−3−3−3333300000000
χ21222222-12-2-2-2-2222-1-1-1-1-1-1-111111111-2-200000000-1-1-1-11111−3−3−3−3−3−3−3−33333333322-2-20000-1-1-1-11111−3−3−3−3333300000000
χ22222222-12-2-2-2-2222-1-1-1-1-1-1-111111111-2-200000000-1-1-1-11111−3−3−3−3−3−3−3−333333333-2-22200001111-1-1-1-13333−3−3−3−300000000
χ232222-2-22222-2-22-2-2-2-2-2-22222222-2-2-2-22-20000000022-2-222-2-2000000000000000000002i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i00000000
χ242222-2-22222-2-22-2-2-2-2-2-22222222-2-2-2-22-20000000022-2-222-2-200000000000000000000−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i00000000
χ252222-2-222-2-2222-2-2-2-2-2-2222-2-2-2-22222-222222-2-2-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ262222-2-222-2-2222-2-2-2-2-2-2222-2-2-2-22222-22-2-2-2-2222222-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ272222-2-22-222-2-2-222-2-2-2-22222222-2-2-2-2-2200000000-2-222-2-222000000000000000000000000000000000000000000002-200
χ282222-2-22-222-2-2-222-2-2-2-22222222-2-2-2-2-2200000000-2-222-2-22200000000000000000000000000000000000000000000-2200
χ292222-2-22-2-2-222-222-2-2-2-2222-2-2-2-222222-200000000-2-22222-2-200000000000000000000000000000000000000002-2000000
χ302222-2-22-2-2-222-222-2-2-2-2222-2-2-2-222222-200000000-2-22222-2-20000000000000000000000000000000000000000-22000000
χ312222-2-2-1222-2-22-2-21111-1-1-1-1-1-1-111112-200000000-1-111-1-1113333−3−3−3−3−3−3−3−3333300002i2i−2i−2i−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii00000000
χ322222-2-2-1222-2-22-2-21111-1-1-1-1-1-1-111112-200000000-1-111-1-1113333−3−3−3−3−3−3−3−333330000−2i−2i2i2ii3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i00000000
χ332222-2-2-1222-2-22-2-21111-1-1-1-1-1-1-111112-200000000-1-111-1-111−3−3−3−333333333−3−3−3−300002i2i−2i−2ii3i3−i3−i3i3i3−i3−i3−i−iii−i−iii00000000
χ342222-2-2-1222-2-22-2-21111-1-1-1-1-1-1-111112-200000000-1-111-1-111−3−3−3−333333333−3−3−3−30000−2i−2i2i2i−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i00000000
χ352222-2-2-12-2-2222-2-21111-1-1-11111-1-1-1-1-222222-2-2-2-2-1-11111-1-1-1-1-1-11111-1-1-1-1111100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000
χ362222-2-2-12-2-2222-2-21111-1-1-11111-1-1-1-1-222222-2-2-2-2-1-11111-1-1-1-1-1-11111-1-1-1-1111100000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000
χ372222-2-2-12-2-2222-2-21111-1-1-11111-1-1-1-1-22-2-2-2-22222-1-11111-1-11111-1-1-1-11111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000
χ382222-2-2-12-2-2222-2-21111-1-1-11111-1-1-1-1-22-2-2-2-22222-1-11111-1-11111-1-1-1-11111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000
χ3922-2-22-22-2000022-222-2-2-22-20000000000−i2−i2i2i2−i2−i2i2i22-22-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002i−2i2−22−200002i−2i2i−2i2−22−22−22−200000000
χ4022-2-22-22-2000022-222-2-2-22-20000000000−i2−i2i2i2−i2−i2i2i22-22-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200−2i2i−22−220000−2i2i−2i2i−22−22−22−2200000000
χ4122-2-22-22-2000022-222-2-2-22-20000000000i2i2−i2−i2i2i2−i2−i22-22-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002i−2i−22−2200002i−2i2i−2i−22−22−22−2200000000
χ4222-2-22-22-2000022-222-2-2-22-20000000000i2i2−i2−i2i2i2−i2−i22-22-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200−2i2i2−22−20000−2i2i−2i2i2−22−22−22−200000000
χ4322-2-22-2-1-2000022-2-1-1111-1133−3−33−33−300−i2−i2i2i2−i2−i2i2i2-11-113−33−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23002i−2i2−22−2−i3i3−i3i3−ii−iiζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300000000
χ4422-2-22-2-1-2000022-2-1-1111-1133−3−33−33−300−i2−i2i2i2−i2−i2i2i2-11-113−33−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300−2i2i−22−22i3−i3i3−i3i−ii−i−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300000000
χ4522-2-22-2-1-2000022-2-1-1111-1133−3−33−33−300i2i2−i2−i2i2i2−i2−i2-11-113−33−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23002i−2i−22−22−i3i3−i3i3−ii−ii−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300000000
χ4622-2-22-2-1-2000022-2-1-1111-1133−3−33−33−300i2i2−i2−i2i2i2−i2−i2-11-113−33−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300−2i2i2−22−2i3−i3i3−i3i−ii−iζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300000000
χ4722-2-22-2-1-2000022-2-1-1111-11−3−333−33−3300−i2−i2i2i2−i2−i2i2i2-11-11−33−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7002i−2i2−22−2i3−i3i3−i3−ii−iiζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700000000
χ4822-2-22-2-1-2000022-2-1-1111-11−3−333−33−3300−i2−i2i2i2−i2−i2i2i2-11-11−33−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700−2i2i−22−22−i3i3−i3i3i−ii−i−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700000000
χ4922-2-22-2-1-2000022-2-1-1111-11−3−333−33−3300i2i2−i2−i2i2i2−i2−i2-11-11−33−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7002i−2i−22−22i3−i3i3−i3−ii−ii−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700000000
χ5022-2-22-2-1-2000022-2-1-1111-11−3−333−33−3300i2i2−i2−i2i2i2−i2−i2-11-11−33−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700−2i2i2−22−2−i3i3−i3i3i−ii−iζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700000000
χ5122-2-2-222-200002-22-2-222-22-20000000000−i2−i2i2i2i2i2−i2−i22-2-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i22-200−i2i2i2−i2-222-20000−i2i2i2−i2−i2i2i2−i200000000
χ5222-2-2-222-200002-22-2-222-22-20000000000−i2−i2i2i2i2i2−i2−i22-2-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2-2200i2−i2−i2i22-2-220000i2−i2−i2i2i2−i2−i2i200000000
χ5322-2-2-222-200002-22-2-222-22-20000000000i2i2−i2−i2−i2−i2i2i22-2-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i22-200i2−i2−i2i2-222-20000i2−i2−i2i2i2−i2−i2i200000000
χ5422-2-2-222-200002-22-2-222-22-20000000000i2i2−i2−i2−i2−i2i2i22-2-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2-2200−i2i2i2−i22-2-220000−i2i2i2−i2−i2i2i2−i200000000
χ5522-2-2-22-1-200002-2211-1-11-1133−3−3−33−3300−i2−i2i2i2i2i2−i2−i2-111-13−3−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ72-200−i2i2i2−i21-1-11−333−3ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ700000000
χ5622-2-2-22-1-200002-2211-1-11-1133−3−3−33−3300−i2−i2i2i2i2i2−i2−i2-111-13−3−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7-2200i2−i2−i2i2-111-13−3−33−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ700000000
χ5722-2-2-22-1-200002-2211-1-11-1133−3−3−33−3300i2i2−i2−i2−i2−i2i2i2-111-13−3−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ72-200i2−i2−i2i21-1-11−333−3−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ700000000
χ5822-2-2-22-1-200002-2211-1-11-1133−3−3−33−3300i2i2−i2−i2−i2−i2i2i2-111-13−3−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7-2200−i2i2i2−i2-111-13−3−33ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ700000000
χ5922-2-2-22-1-200002-2211-1-11-11−3−3333−33−300−i2−i2i2i2i2i2−i2−i2-111-1−333−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ232-200−i2i2i2−i21-1-113−3−33ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ2300000000
χ6022-2-2-22-1-200002-2211-1-11-11−3−3333−33−300−i2−i2i2i2i2i2−i2−i2-111-1−333−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23-2200i2−i2−i2i2-111-1−333−3−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ2300000000
χ6122-2-2-22-1-200002-2211-1-11-11−3−3333−33−300i2i2−i2−i2−i2−i2i2i2-111-1−333−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ232-200i2−i2−i2i21-1-113−3−33−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ2300000000
χ6222-2-2-22-1-200002-2211-1-11-11−3−3333−33−300i2i2−i2−i2−i2−i2i2i2-111-1−333−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23-2200−i2i2i2−i2-111-1−333−3ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ2300000000
χ63444444-2-44444-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-4-40000000022222222000000000000000000000000000000000000000000000000
χ64444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-22222222244000000002222-2-2-2-2000000000000000000000000000000000000000000000000
χ654444-4-4-2-444-4-4-4442222-2-2-2-2-2-2-22222-440000000022-2-222-2-2000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.