Finite Group Databasebeta

← Group #13147023

Character table — Group #13147023

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111122222222233333366666666666666666666666666666666666666666242424242424242424242424242424242424242424242424727272727272727272727272
order123366488121224242424226666346666666881212121212121212121224242424242424242424242424242424242424243336661212121212122424242424242424242424242244666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111-1-111-1-1-1-1111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ41111111-1-111-1-1-1-1111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ522222222222222222222222222222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ6222222222222222222222-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-122-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ7222222222222222222222-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-1-122-1-1-1-1-1-12222-1-1-1-1000000000000
χ8222222222222222222222-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1-12222000000000000
χ92222222-2-222-2-2-2-2222222222222222-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000
χ102222222-2-222-2-2-2-2222222-12-1-1-1-1-1-1-1-2-222-1-1-1-1-1-1-1-1-2-2-2-211111111111111112-1-12-1-122-1-1-1-1-2-2-2-211111111000000000000
χ112222222-2-222-2-2-2-2222222-12-1-1-1-1-1-1-1-2-222-1-1-1-1-1-1-1-1-2-2-2-21111111111111111-12-1-12-1-1-122-1-11111-2-2-2-21111000000000000
χ122222222-2-222-2-2-2-2222222-12-1-1-1-1-1-1-1-2-222-1-1-1-1-1-1-1-1-2-2-2-21111111111111111-1-12-1-12-1-1-1-12211111111-2-2-2-2000000000000
χ13222222-200-2-200002222222-2222222200-2-2-2-2-2-2-2-2-2-200000000000000000000222222-2-2-2-2-2-2000000000000000000000000
χ14222222-200-2-200002222222-2222222200-2-2-2-2-2-2-2-2-2-200000000000000000000-1-1-1-1-1-111111133−3−333−3−333−3−3000000000000
χ15222222-200-2-200002222222-2222222200-2-2-2-2-2-2-2-2-2-200000000000000000000-1-1-1-1-1-1111111−3−333−3−333−3−333000000000000
χ16222222-200-2-20000222222-1-2-1-1-1-1-1-1-100-2-211111111000033333333−3−3−3−3−3−3−3−32-1-12-1-1-2-21111000033−3−3−3−333000000000000
χ17222222-200-2-20000222222-1-2-1-1-1-1-1-1-100-2-211111111000033333333−3−3−3−3−3−3−3−3-12-1-12-111-2-211−3−333000033−3−3000000000000
χ18222222-200-2-20000222222-1-2-1-1-1-1-1-1-100-2-211111111000033333333−3−3−3−3−3−3−3−3-1-12-1-121111-2-233−3−3−3−3330000000000000000
χ19222222-200-2-20000222222-1-2-1-1-1-1-1-1-100-2-2111111110000−3−3−3−3−3−3−3−3333333332-1-12-1-1-2-211110000−3−33333−3−3000000000000
χ20222222-200-2-20000222222-1-2-1-1-1-1-1-1-100-2-2111111110000−3−3−3−3−3−3−3−333333333-12-1-12-111-2-21133−3−30000−3−333000000000000
χ21222222-200-2-20000222222-1-2-1-1-1-1-1-1-100-2-2111111110000−3−3−3−3−3−3−3−333333333-1-12-1-121111-2-2−3−33333−3−30000000000000000
χ222-222-2-202−20022−2−2-22-2-22220222-2-2-2-22−2000000000022−2−22222−2−2−2−22222−2−2−2−2222-2-2-20000002−22−22−22−22−22−2000000000000
χ232-222-2-202−20022−2−2-22-2-22220222-2-2-2-22−2000000000022−2−22222−2−2−2−22222−2−2−2−2-1-1-11113−33−33−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ242-222-2-202−20022−2−2-22-2-22220222-2-2-2-22−2000000000022−2−22222−2−2−2−22222−2−2−2−2-1-1-1111−33−33−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ252-222-2-202−20022−2−2-22-2-222-10-1-1-111112−200333−3−3−33−322−2−2ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ232-1-1-211003−3−332−22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ262-222-2-202−20022−2−2-22-2-222-10-1-1-111112−200333−3−3−33−322−2−2ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23-12-11-21−33003−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ272-222-2-202−20022−2−2-22-2-222-10-1-1-111112−200333−3−3−33−322−2−2ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23-1-1211-23−3−3300ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−22−2000000000000
χ282-222-2-202−20022−2−2-22-2-222-10-1-1-111112−200−3−3−3333−3322−2−2ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ72-1-1-21100−333−32−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ292-222-2-202−20022−2−2-22-2-222-10-1-1-111112−200−3−3−3333−3322−2−2ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7-12-11-213−300−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ302-222-2-202−20022−2−2-22-2-222-10-1-1-111112−200−3−3−3333−3322−2−2ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7-1-1211-2−333−300ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−22−2000000000000
χ312-222-2-20−2200−2−222-22-2-22220222-2-2-2-2−220000000000−2−222−2−2−2−22222−2−2−2−22222222-2-2-2000000−22−22−22−22−22−22000000000000
χ322-222-2-20−2200−2−222-22-2-22220222-2-2-2-2−220000000000−2−222−2−2−2−22222−2−2−2−22222-1-1-11113−33−33−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ332-222-2-20−2200−2−222-22-2-22220222-2-2-2-2−220000000000−2−222−2−2−2−22222−2−2−2−22222-1-1-1111−33−33−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ342-222-2-20−2200−2−222-22-2-222-10-1-1-11111−2200333−3−3−33−3−2−222−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ232-1-1-211003−3−33−22−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ352-222-2-20−2200−2−222-22-2-222-10-1-1-11111−2200333−3−3−33−3−2−222−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23-12-11-21−33003−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ362-222-2-20−2200−2−222-22-2-222-10-1-1-11111−2200333−3−3−33−3−2−222−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23-1-1211-23−3−3300−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−22000000000000
χ372-222-2-20−2200−2−222-22-2-222-10-1-1-11111−2200−3−3−3333−33−2−222−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ72-1-1-21100−333−3−22−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ382-222-2-20−2200−2−222-22-2-222-10-1-1-11111−2200−3−3−3333−33−2−222−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7-12-11-213−300−33−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ392-222-2-20−2200−2−222-22-2-222-10-1-1-11111−2200−3−3−3333−33−2−222−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7-1-1211-2−333−300−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−22000000000000
χ40333333333333333-1-1-1-1-1-13-1-1-1-1-1-1-13-1-1-1-1-1-1-1-1-1-133-1-1-1-13-1-1-13-1-1-13-1-1-13-1-1-100000000000000000000000011-1-11111-1-1-1-1
χ41333333333333333-1-1-1-1-1-13-1-1-1-1-1-1-13-1-1-1-1-1-1-1-1-1-133-1-1-1-13-1-1-13-1-1-13-1-1-13-1-1-1000000000000000000000000-1-111-1-1-1-11111
χ423333333-3-333-3-3-3-3-1-1-1-1-1-13-1-1-1-1-1-1-1311-1-1-1-1-1-1-1-1331111-3111-3111-3111-31110000000000000000000000001-1-1111-1-1-1-111
χ433333333-3-333-3-3-3-3-1-1-1-1-1-13-1-1-1-1-1-1-1311-1-1-1-1-1-1-1-1331111-3111-3111-3111-3111000000000000000000000000-111-1-1-11111-1-1
χ4433−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3203000000033−3−3i32−3+3i3200000000−3−3i32−3+3i32−3−3i32−3+3i3200000000000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ4533−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3203000000033−3−3i32−3+3i3200000000−3−3i32−3+3i32−3−3i32−3+3i320000000000000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32
χ4633−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321−i321+i321−i320-12−1−i3−1+i32−1−i3−1+i30-1-11+i321−i322−1−i3−1+i32−1−i3−1+i3001+i321−i321+i321−i3202−1−i3−1+i302−1−i3−1+i302−1−i3−1+i302−1−i3−1+i300000000000000000000000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ4733−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-11+i321−i321+i321−i320-12−1−i3−1+i32−1−i3−1+i30-1-11+i321−i322−1−i3−1+i32−1−i3−1+i3001+i321−i321+i321−i3202−1−i3−1+i302−1−i3−1+i302−1−i3−1+i302−1−i3−1+i3000000000000000000000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ4833−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i3233−3−3i32−3+3i32−3−3i32−3+3i32030000000-3-3−3−3i32−3+3i32000000003+3i323−3i323+3i323−3i3200000000000000000000000000000000000000001-11-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32
χ4933−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i3233−3−3i32−3+3i32−3−3i32−3+3i32030000000-3-3−3−3i32−3+3i32000000003+3i323−3i323+3i323−3i320000000000000000000000000000000000000000-11-111+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32
χ5033−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-1-11+i321−i321+i321−i320-12−1−i3−1+i32−1−i3−1+i30111+i321−i322−1−i3−1+i32−1−i3−1+i300−1−i32−1+i32−1−i32−1+i320-21+i31−i30-21+i31−i30-21+i31−i30-21+i31−i30000000000000000000000001-1-11−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32
χ5133−3−3i32−3+3i32−3−3i32−3+3i323-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-1-11+i321−i321+i321−i320-12−1−i3−1+i32−1−i3−1+i30111+i321−i322−1−i3−1+i32−1−i3−1+i300−1−i32−1+i32−1−i32−1+i320-21+i31−i30-21+i31−i30-21+i31−i30-21+i31−i3000000000000000000000000-111-11+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i32
χ5233−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3203000000033−3+3i32−3−3i3200000000−3+3i32−3−3i32−3+3i32−3−3i3200000000000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ5333−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3203000000033−3+3i32−3−3i3200000000−3+3i32−3−3i32−3+3i32−3−3i320000000000000000000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32
χ5433−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321+i321−i321+i320-12−1+i3−1−i32−1+i3−1−i30-1-11−i321+i322−1+i3−1−i32−1+i3−1−i3001−i321+i321−i321+i3202−1+i3−1−i302−1+i3−1−i302−1+i3−1−i302−1+i3−1−i300000000000000000000000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
χ5533−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-1-11−i321+i321−i321+i320-12−1+i3−1−i32−1+i3−1−i30-1-11−i321+i322−1+i3−1−i32−1+i3−1−i3001−i321+i321−i321+i3202−1+i3−1−i302−1+i3−1−i302−1+i3−1−i302−1+i3−1−i3000000000000000000000000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32
χ5633−3+3i32−3−3i32−3+3i32−3−3i323-3-3−3+3i32−3−3i323−3i323+3i323−3i323+3i3233−3+3i32−3−3i32−3+3i32−3−3i32030000000-3-3−3+3i32−3−3i32000000003−3i323+3i323−3i323+3i3200000000000000000000000000000000000000001-11-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.