Finite Group Databasebeta

← Group #10698618

Character table — Group #10698618

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order122222223444444446666666121212121212121244888888881212121212121212242424242424242424242424242424244444888812121212121212122424242424242424444488884444
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
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111
χ9222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000022-2-200002222-2-2-2-200000000000000000000
χ10222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000000000-2-2220000-2-2-2-2222200000000000000000000
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
χ13222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-2-2-22222000000000000000000000000000000000000000000000000002-2
χ14222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-2-2-2222200000000000000000000000000000000000000000000000000-22
χ1522222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ1622222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000
χ1722222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ1822222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ1922222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-1111133333333−3−3−3−3−3−3−3−322-2-20000-1-1-1-111113333−3−3−3−3000000000000
χ2022222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-1111133333333−3−3−3−3−3−3−3−3-2-22200001111-1-1-1-1−3−3−3−33333000000000000
χ2122222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-11111−3−3−3−3−3−3−3−33333333322-2-20000-1-1-1-11111−3−3−3−33333000000000000
χ2222222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-11111−3−3−3−3−3−3−3−333333333-2-22200001111-1-1-1-13333−3−3−3−3000000000000
χ232222-2-2-2-2222-20000-22-22-2-22-200000000002222−2−2−2−222-2-200002222−2−2−2−22222−2−2−2−2002-222−2−2000022-2-222−2−222−2−2000000000000
χ242222-2-2-2-2222-20000-22-22-2-22-200000000002222−2−2−2−222-2-200002222−2−2−2−22222−2−2−2−200-22−2−2220000-2-222−2−222−2−222000000000000
χ252222-2-2-2-2222-20000-22-22-2-22-20000000000−2−2−2−2222222-2-20000−2−2−2−22222−2−2−2−22222002-2−2−222000022-2-2−2−222−2−222000000000000
χ262222-2-2-2-2222-20000-22-22-2-22-20000000000−2−2−2−2222222-2-20000−2−2−2−22222−2−2−2−2222200-2222−2−20000-2-22222−2−222−2−2000000000000
χ272222-2-2-2-2-122-20000-2-11-111-11333−3−3−33−3002222−2−2−2−2-1-1113−33−3ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23002-222−2−233−3−3-1-111ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ282222-2-2-2-2-122-20000-2-11-111-11333−3−3−33−3002222−2−2−2−2-1-1113−33−3ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ2300-22−2−222−3−33311-1-1−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ292222-2-2-2-2-122-20000-2-11-111-11333−3−3−33−300−2−2−2−22222-1-1113−33−3−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23002-2−2−22233−3−3-1-111−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ302222-2-2-2-2-122-20000-2-11-111-11333−3−3−33−300−2−2−2−22222-1-1113−33−3−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ2300-2222−2−2−3−33311-1-1ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ312222-2-2-2-2-122-20000-2-11-111-11−3−3−3333−33002222−2−2−2−2-1-111−33−33ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7002-222−2−2−3−333-1-111ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ322222-2-2-2-2-122-20000-2-11-111-11−3−3−3333−33002222−2−2−2−2-1-111−33−33ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ700-22−2−22233−3−311-1-1−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ332222-2-2-2-2-122-20000-2-11-111-11−3−3−3333−3300−2−2−2−22222-1-111−33−33−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7002-2−2−222−3−333-1-111−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ342222-2-2-2-2-122-20000-2-11-111-11−3−3−3333−3300−2−2−2−22222-1-111−33−33−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ700-2222−2−233−3−311-1-1ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ3522-2-2-2-222200022-2-2022-22-2-2-222-222-2-2-20022−2−222−2−20000000022−2−222−2−222−2−222−2−20000000000000000000000002i−2i00−i2−i2i2i20000
χ3622-2-2-2-222200022-2-2022-22-2-2-222-222-2-2-20022−2−222−2−20000000022−2−222−2−222−2−222−2−2000000000000000000000000−2i2i00i2i2−i2−i20000
χ3722-2-2-2-222200022-2-2022-22-2-2-222-222-2-2-200−2−222−2−22200000000−2−222−2−222−2−222−2−2220000000000000000000000002i−2i00i2i2−i2−i20000
χ3822-2-2-2-222200022-2-2022-22-2-2-222-222-2-2-200−2−222−2−22200000000−2−222−2−222−2−222−2−222000000000000000000000000−2i2i00−i2−i2i2i20000
χ392-22-22-22-222-2-200002-222-2-2-220000000000−i2i2−i2i2−i2i2−i2i22-22-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22-200−i2i2−i2i22-22-20000−i2i2−i2i2−i2i2−i2i2000000000000
χ402-22-22-22-222-2-200002-222-2-2-220000000000−i2i2−i2i2−i2i2−i2i22-22-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2-2200i2−i2i2−i2-22-220000i2−i2i2−i2i2−i2i2−i2000000000000
χ412-22-22-22-222-2-200002-222-2-2-220000000000i2−i2i2−i2i2−i2i2−i22-22-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22-200i2−i2i2−i22-22-20000i2−i2i2−i2i2−i2i2−i2000000000000
χ422-22-22-22-222-2-200002-222-2-2-220000000000i2−i2i2−i2i2−i2i2−i22-22-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2-2200−i2i2−i2i2-22-220000−i2i2−i2i2−i2i2−i2i2000000000000
χ432-22-22-22-2-12-2-2000021-1-1111-13−333−3−3−3300−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−i2i2−i2i2-11-113−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ442-22-22-22-2-12-2-2000021-1-1111-13−333−3−3−3300−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−ζ23-2200i2−i2i2−i21-11-1−33−33−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ452-22-22-22-2-12-2-2000021-1-1111-13−333−3−3−3300i2−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+ζ232-200i2−i2i2−i2-11-113−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ462-22-22-22-2-12-2-2000021-1-1111-13−333−3−3−3300i2−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+ζ23-2200−i2i2−i2i21-11-1−33−33ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ472-22-22-22-2-12-2-2000021-1-1111-1−33−3−3333−300−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−i2i2−i2i2-11-11−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ482-22-22-22-2-12-2-2000021-1-1111-1−33−3−3333−300−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−ζ7-2200i2−i2i2−i21-11-13−33−3−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ492-22-22-22-2-12-2-2000021-1-1111-1−33−3−3333−300i2−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+ζ72-200i2−i2i2−i2-11-11−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ502-22-22-22-2-12-2-2000021-1-1111-1−33−3−3333−300i2−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+ζ7-2200−i2i2−i2i21-11-13−33−3ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ512-22-2-22-2222-222-22-2-2-2-2222-2-22-22-222-2-2-22000000002-2-22-2-222000000000000000000002i−2i−2i2i000000002i−2i−2i2i2i−2i−2i2i000000000000
χ522-22-2-22-2222-222-22-2-2-2-2222-2-22-22-222-2-2-22000000002-2-22-2-22200000000000000000000−2i2i2i−2i00000000−2i2i2i−2i−2i2i2i−2i000000000000
χ532-22-2-22-2222-22-22-22-2-2-2222-2-2-22-22-2-2222-22i−2i2i−2i−2i2i−2i2i2-2-2222-2-22i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ542-22-2-22-2222-22-22-22-2-2-2222-2-2-22-22-2-2222-2−2i2i−2i2i2i−2i2i−2i2-2-2222-2-2−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ552-22-2-22-222-22-22-22-22-2-2222-2-22-22-222-2-22-200000000-222-222-2-20000000000000000000000000000000000000000000000002i−2i00
χ562-22-2-22-222-22-22-22-22-2-2222-2-22-22-222-2-22-200000000-222-222-2-2000000000000000000000000000000000000000000000000−2i2i00
χ572-22-2-22-222-22-2-22-222-2-2222-2-2-22-22-2-222-2200000000-222-2-2-222000000000000000000000000000000000000000000002-22-20000
χ582-22-2-22-222-22-2-22-222-2-2222-2-2-22-22-2-222-2200000000-222-2-2-22200000000000000000000000000000000000000000000-22-220000
χ592-22-2-22-22-12-222-22-2-211-1-1-111-11-11-1-111-2200000000-111-111-1-1−i3i3−i3i3i3−i3i3−i3i3−i3i3−i3−i3i3−i3i300002i−2i−2i2i−333−33−3−33−iii−i−iii−i000000000000
χ602-22-2-22-22-12-222-22-2-211-1-1-111-11-11-1-111-2200000000-111-111-1-1−i3i3−i3i3i3−i3i3−i3i3−i3i3−i3−i3i3−i3i30000−2i2i2i−2i3−3−33−333−3i−i−iii−i−ii000000000000
χ612-22-2-22-22-12-222-22-2-211-1-1-111-11-11-1-111-2200000000-111-111-1-1i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3i3−i3i3−i300002i−2i−2i2i3−3−33−333−3−iii−i−iii−i000000000000
χ622-22-2-22-22-12-222-22-2-211-1-1-111-11-11-1-111-2200000000-111-111-1-1i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3i3−i3i3−i30000−2i2i2i−2i−333−33−3−33i−i−iii−i−ii000000000000
χ632-22-2-22-22-12-22-22-22-211-1-1-1111-11-111-1-12-22i−2i2i−2i−2i2i−2i2i-111-1-1-111−ii−iii−ii−i−ii−iii−ii−i000000003−3−333−3−33−i3i3i3−i3i3−i3−i3i3000000000000
χ642-22-2-22-22-12-22-22-22-211-1-1-1111-11-111-1-12-22i−2i2i−2i−2i2i−2i2i-111-1-1-111−ii−iii−ii−i−ii−iii−ii−i00000000−333−3−333−3i3−i3−i3i3−i3i3i3−i3000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.