Finite Group Databasebeta

← Group #10696952

Character table — Group #10696952

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444448888888888888888888888884848484848484848
order12222234444444466612121212121212121212121244668888888812121212121224242424242424242424242424242424888888882424242424242424242424242424242422244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
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
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ922222222-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-2220000000022-2-2-2-2000000000000000022-2-200002222-2-2-2-20000000000000000
χ1022222222-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-2220000000022-2-2-2-20000000000000000-2-2220000-2-2-2-222220000000000000000
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
χ132222222-2-2-222-2-2-2222-2-2-2-2-2-2-2-22222-222200000000-2-2-2-222000000000000000000000000000000000000000000002-200
χ142222222-2-2-222-2-2-2222-2-2-2-2-2-2-2-22222-222200000000-2-2-2-22200000000000000000000000000000000000000000000-2200
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
χ19222222-12-2-2-2-2222-1-1-11111-1-1-1-11111-2-2-1-100000000-1-1111133333333−3−3−3−3−3−3−3−322-2-20000-1-1-1-111113333−3−3−3−300000000
χ20222222-12-2-2-2-2222-1-1-11111-1-1-1-11111-2-2-1-100000000-1-1111133333333−3−3−3−3−3−3−3−3-2-22200001111-1-1-1-1−3−3−3−3333300000000
χ21222222-12-2-2-2-2222-1-1-11111-1-1-1-11111-2-2-1-100000000-1-11111−3−3−3−3−3−3−3−33333333322-2-20000-1-1-1-11111−3−3−3−3333300000000
χ22222222-12-2-2-2-2222-1-1-11111-1-1-1-11111-2-2-1-100000000-1-11111−3−3−3−3−3−3−3−333333333-2-22200001111-1-1-1-13333−3−3−3−300000000
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
χ252222-2-222-2-222-2-22222-2-2-2-2-2-2-2-222222-2-2-2000000002222-2-20000000000000000000022-2-20000000022-2-222-2-200000000
χ262222-2-222-2-222-2-22222-2-2-2-2-2-2-2-222222-2-2-2000000002222-2-200000000000000000000-2-22200000000-2-222-2-22200000000
χ272222-2-22-2222222-2222222222222222-2-2-2-200000000-2-2-2-2-2-20000000000000000000000000000000000000000002-20000
χ282222-2-22-2222222-2222222222222222-2-2-2-200000000-2-2-2-2-2-2000000000000000000000000000000000000000000-220000
χ292222-2-22-2-2-2-2-222-2222-2-2-2-22222-2-2-2-222-2-200000000-2-2222200000000000000000000000000000000000000002-2000000
χ302222-2-22-2-2-2-2-222-2222-2-2-2-22222-2-2-2-222-2-200000000-2-222220000000000000000000000000000000000000000-22000000
χ312222-2-2-1222-2-2-2-22-1-1-1-1-1-1-111111111-22112222-2-2-2-2-1-111-1-1-1-1-1-11111-1-1-1-111110000000033−3−333−3−333−3−3−3−33300000000
χ322222-2-2-1222-2-2-2-22-1-1-1-1-1-1-111111111-22112222-2-2-2-2-1-111-1-1-1-1-1-11111-1-1-1-1111100000000−3−333−3−333−3−33333−3−300000000
χ332222-2-2-1222-2-2-2-22-1-1-1-1-1-1-111111111-2211-2-2-2-22222-1-111-1-11111-1-1-1-11111-1-1-1-10000000033−3−333−3−3−3−33333−3−300000000
χ342222-2-2-1222-2-2-2-22-1-1-1-1-1-1-111111111-2211-2-2-2-22222-1-111-1-11111-1-1-1-11111-1-1-1-100000000−3−333−3−33333−3−3−3−33300000000
χ352222-2-2-12-2-222-2-22-1-1-111111111-1-1-1-12-21100000000-1-1-1-1113333−3−3−3−3−3−3−3−33333000022-2-2−3−33333−3−3-1-111-1-11100000000
χ362222-2-2-12-2-222-2-22-1-1-111111111-1-1-1-12-21100000000-1-1-1-1113333−3−3−3−3−3−3−3−333330000-2-22233−3−3−3−33311-1-111-1-100000000
χ372222-2-2-12-2-222-2-22-1-1-111111111-1-1-1-12-21100000000-1-1-1-111−3−3−3−333333333−3−3−3−3000022-2-233−3−3−3−333-1-111-1-11100000000
χ382222-2-2-12-2-222-2-22-1-1-111111111-1-1-1-12-21100000000-1-1-1-111−3−3−3−333333333−3−3−3−30000-2-222−3−33333−3−311-1-111-1-100000000
χ392-22-22-22200002-2-22-2-2000022-2-20000002-2−i2−i2i2i2−i2−i2i2i22-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002-2−i2i2−i2i200002-22-2−i2i2−i2i2−i2i2−i2i200000000
χ402-22-22-22200002-2-22-2-2000022-2-20000002-2−i2−i2i2i2−i2−i2i2i22-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200-22i2−i2i2−i20000-22-22i2−i2i2−i2i2−i2i2−i200000000
χ412-22-22-22200002-2-22-2-2000022-2-20000002-2i2i2−i2−i2i2i2−i2−i22-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002-2i2−i2i2−i200002-22-2i2−i2i2−i2i2−i2i2−i200000000
χ422-22-22-22200002-2-22-2-2000022-2-20000002-2i2i2−i2−i2i2i2−i2−i22-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200-22−i2i2−i2i20000-22-22−i2i2−i2i2−i2i2−i2i200000000
χ432-22-22-2-1200002-2-2-11133−3−3-1-11133−3−300-11−i2−i2i2i2−i2−i2i2i2-113−33−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23002-2−i2i2−i2i23−33−3-11-11ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ700000000
χ442-22-22-2-1200002-2-2-11133−3−3-1-11133−3−300-11−i2−i2i2i2−i2−i2i2i2-113−33−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300-22i2−i2i2−i2−33−331-11-1−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ700000000
χ452-22-22-2-1200002-2-2-11133−3−3-1-11133−3−300-11i2i2−i2−i2i2i2−i2−i2-113−33−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23002-2i2−i2i2−i23−33−3-11-11−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ700000000
χ462-22-22-2-1200002-2-2-11133−3−3-1-11133−3−300-11i2i2−i2−i2i2i2−i2−i2-113−33−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300-22−i2i2−i2i2−33−331-11-1ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ700000000
χ472-22-22-2-1200002-2-2-111−3−333-1-111−3−33300-11−i2−i2i2i2−i2−i2i2i2-11−33−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7002-2−i2i2−i2i2−33−33-11-11ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ2300000000
χ482-22-22-2-1200002-2-2-111−3−333-1-111−3−33300-11−i2−i2i2i2−i2−i2i2i2-11−33−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700-22i2−i2i2−i23−33−31-11-1−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ2300000000
χ492-22-22-2-1200002-2-2-111−3−333-1-111−3−33300-11i2i2−i2−i2i2i2−i2−i2-11−33−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7002-2i2−i2i2−i2−33−33-11-11−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ2300000000
χ502-22-22-2-1200002-2-2-111−3−333-1-111−3−33300-11i2i2−i2−i2i2i2−i2−i2-11−33−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700-22−i2i2−i2i23−33−31-11-1ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ2300000000
χ512-22-2-22220000-22-22-2-20000-2-222000000-22−i2−i2i2i2i2i2−i2−i22-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i22-200−i2i2i2−i22-2-220000−i2i2i2−i2−i2i2i2−i200000000
χ522-22-2-22220000-22-22-2-20000-2-222000000-22−i2−i2i2i2i2i2−i2−i22-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2-2200i2−i2−i2i2-222-20000i2−i2−i2i2i2−i2−i2i200000000
χ532-22-2-22220000-22-22-2-20000-2-222000000-22i2i2−i2−i2−i2−i2i2i22-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i22-200i2−i2−i2i22-2-220000i2−i2−i2i2i2−i2−i2i200000000
χ542-22-2-22220000-22-22-2-20000-2-222000000-22i2i2−i2−i2−i2−i2i2i22-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2-2200−i2i2i2−i2-222-20000−i2i2i2−i2−i2i2i2−i200000000
χ552-22-2-22-120000-22-2-11133−3−311-1-1−3−333001-1−i2−i2i2i2i2i2−i2−i2-11−333−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ232-200−i2i2i2−i2-111-1−333−3ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ2300000000
χ562-22-2-22-120000-22-2-11133−3−311-1-1−3−333001-1−i2−i2i2i2i2i2−i2−i2-11−333−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23-2200i2−i2−i2i21-1-113−3−33−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ2300000000
χ572-22-2-22-120000-22-2-11133−3−311-1-1−3−333001-1i2i2−i2−i2−i2−i2i2i2-11−333−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ232-200i2−i2−i2i2-111-1−333−3−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ2300000000
χ582-22-2-22-120000-22-2-11133−3−311-1-1−3−333001-1i2i2−i2−i2−i2−i2i2i2-11−333−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23-2200−i2i2i2−i21-1-113−3−33ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ2300000000
χ592-22-2-22-120000-22-2-111−3−33311-1-133−3−3001-1−i2−i2i2i2i2i2−i2−i2-113−3−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ72-200−i2i2i2−i2-111-13−3−33ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ700000000
χ602-22-2-22-120000-22-2-111−3−33311-1-133−3−3001-1−i2−i2i2i2i2i2−i2−i2-113−3−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7-2200i2−i2−i2i21-1-11−333−3−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ700000000
χ612-22-2-22-120000-22-2-111−3−33311-1-133−3−3001-1i2i2−i2−i2−i2−i2i2i2-113−3−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ72-200i2−i2−i2i2-111-13−3−33−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ700000000
χ622-22-2-22-120000-22-2-111−3−33311-1-133−3−3001-1i2i2−i2−i2−i2−i2i2i2-113−3−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7-2200−i2i2i2−i21-1-11−333−3ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ700000000
χ63444444-2-444-4-4-4-4-4-2-2-2-2-2-2-2222222224-4-2-20000000022-2-222000000000000000000000000000000000000000000000000
χ64444444-2-4-4-444-4-4-4-2-2-222222222-2-2-2-2-44-2-2000000002222-2-2000000000000000000000000000000000000000000000000
χ654444-4-4-2-4444444-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-4-42200000000222222000000000000000000000000000000000000000000000000
χ664444-4-4-2-4-4-4-4-444-4-2-2-22222-2-2-2-2222244220000000022-2-2-2-2000000000000000000000000000000000000000000000000
χ6744-4-40040004-4000-44-4000000004-44-400002i−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.