Finite Group Databasebeta

← Group #13168474

Character table — Group #13168474

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size111122222222222222444444444444444444444466666688888888888812121212121212121212121212121212121212121212121818181818182424242424242424242424242424363636363636363636363654547272108
order12223334466666666633366666666612121212121212121212226666366612121212121212122444466666612121212121212121212121244444466661212121212121212121244412121212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-11-1111111-1-11111-1-11111-1-1-1-1-1-111111-11-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1
χ31111111111111111111111111111111111111111111111111111111111-111-1111111111111111111111-1-111-1-1-1-1-11-11-1-11111-1-1-111-1-1-1-111-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-11-1-1-1111111-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-11
χ51111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-1111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-111111111111111-1-11-1-11111-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-11-111-1-1-1-1-1-1-111-1-1-1-11111-1-11
χ71111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-11-11-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1111111-1-1-1-1-1-1-1-1-111111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-111-1
χ91111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-11-1-1-1-1-1-1111-11-1-111-1-111-1-1-111
χ101111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11-1-111-1-11-1-111-1-111-1-111-11-1
χ111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111-111-1-111-11-1-1-1-1-11111111-1-1
χ121111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1111111-1-1-1111111-1-1-1-1-1-11-11
χ131111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-11-1-1-1-1-1-111-1111111-1-1-1-1111-1-1
χ141111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-1111111-1-111111111-1-11111-1-1-11-1-111-1-1-11-1-1-1-1-11111-1-11-11
χ151111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1111-111-1-1111-1-111-1-111-1-1-1-1-111
χ161111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11-1111111-1-11-11-1-111-1-11111-11-1
χ17222222-1222-12-1222-122-1-12-1-1-1-12-12-122-1-122-1-1-1-1222222-1-1-1-1-1-122-1-1-1-122020-1-1-1-1-1-100-1-12200-1-1-1-10000002-1-1-1-1020-1-100002200000000000-1-10
χ18222222-1222-12-1222-122-1-12-1-1-1-12-12-122-1-122-1-1-1-1222222-1-1-1-1-1-122-1-1-1-1-220-20-1-1-1-1-1-100-1-12200-1-1-1-1000000-211110-20110000-2-200000000000110
χ19222222-1222-12-1222-122-1-12-1-1-1-12-12-122-1-122-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-122-1-1-1-12-20201111110011-2-20011110000002-1-1-1-1020-1-10000-2-200000000000110
χ20222222-1222-12-1222-122-1-12-1-1-1-12-12-122-1-122-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-122-1-1-1-1-2-20-201111110011-2-2001111000000-211110-201100002200000000000-1-10
χ21222222-1-2-22-12-1222-122-1-12-1-1-1-12-12-1-2-211-2-21111222222-1-1-1-111-2-211112-20-20-1-1-1-1-1-10011-2-20011110000002-1-1-110-201100002-2000000000001-10
χ22222222-1-2-22-12-1222-122-1-12-1-1-1-12-12-1-2-211-2-21111222222-1-1-1-111-2-21111-2-2020-1-1-1-1-1-10011-2-2001111000000-2111-1020-1-10000-2200000000000-110
χ23222222-1-2-22-12-1222-122-1-12-1-1-1-12-12-1-2-211-2-21111-2-2-2-2-2-2-1-1-1-111-2-21111220-2011111100-1-12200-1-1-1-10000002-1-1-110-20110000-2200000000000-110
χ24222222-1-2-22-12-1222-122-1-12-1-1-1-12-12-1-2-211-2-21111-2-2-2-2-2-2-1-1-1-111-2-21111-2202011111100-1-12200-1-1-1-1000000-2111-1020-1-100002-2000000000001-10
χ2522222-122222-122-1-122-12-1-122-1-1-1-1-12-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-120222000000220000220000002200-12-1-12-1-1-1-1-1-1-1-1-100200-1-1-1-10000000
χ2622222-122222-122-1-122-12-1-122-1-1-1-1-12-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-120-22-2000000-2-20000-2-2000000-2-200-12-1-121-11-1-1111100-20011110000000
χ2722222-122222-122-1-122-12-1-122-1-1-1-1-12-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-1-202-2200000022000022000000-2-2001-211-2-11-111-1-1-1-100-20011110000000
χ2822222-122222-122-1-122-12-1-122-1-1-1-1-12-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-1-20-2-2-2000000-2-20000-2-200000022001-211-211111111100200-1-1-1-10000000
χ2922222-12-2-222-122-1-122-12-1-122-1-1-1-1-1211-2-2-2-2-2-2-2-2000000-1-1-1-111111111202-2-2000000-2-2000022000000-2-200-12-1-1-2-1111111-1-100200-1-1110000000
χ3022222-12-2-222-122-1-122-12-1-122-1-1-1-1-1211-2-2-2-2-2-2-2-2000000-1-1-1-11111111120-2-22000000220000-2-20000002200-12-1-1-211-111-1-11100-20011-1-10000000
χ3122222-12-2-222-122-1-122-12-1-122-1-1-1-1-1211-2-2-2-2-2-2-2-2000000-1-1-1-111111111-2022-2000000-2-200002200000022001-2112-1-11-1-111-1-100-20011-1-10000000
χ3222222-12-2-222-122-1-122-12-1-122-1-1-1-1-1211-2-2-2-2-2-2-2-2000000-1-1-1-111111111-20-222000000220000-2-2000000-2-2001-21121-1-1-1-1-1-11100200-1-1110000000
χ332222-12222-1222-1222-1-1-12-1-1-122-12-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10220222-1-1-1-1-1-122-1-1-1-1-1-1-1-12200220000020200-1-1-1-1000-1-10000-1-100000
χ342222-12222-1222-1222-1-1-12-1-1-122-12-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-102-20-222-1-1-1-11122-1-111-1-1-1-1-2-200-2-200000-20-20011110001100001100000
χ352222-12222-1222-1222-1-1-12-1-1-122-12-1-12222-1-1-1-1-1-1-2-21111-1-1-1-122-1-1-1-1-1-10-2202-2-21111-1-1-2-211-1-11111-2-200-2-20000020200-1-1-1-10001100001100000
χ362222-12222-1222-1222-1-1-12-1-1-122-12-1-12222-1-1-1-1-1-1-2-21111-1-1-1-122-1-1-1-1-1-10-2-20-2-2-2111111-2-21111111122002200000-20-2001111000-1-10000-1-100000
χ372222-122-2-2-1222-1222-1-1-12-1-1-122-12-1-1-2-2-2-211111122-1-1-1-1-1-1-1-1-2-21111110-220-222-1-1-1-111-2-211-1-111112200-2-20000020-20011-1-1000110000-1-100000
χ382222-122-2-2-1222-1222-1-1-12-1-1-122-12-1-1-2-2-2-211111122-1-1-1-1-1-1-1-1-2-21111110-2-20222-1-1-1-1-1-1-2-211111111-2-2002200000-20200-1-111000-1-100001100000
χ392222-122-2-2-1222-1222-1-1-12-1-1-122-12-1-1-2-2-2-2111111-2-21111-1-1-1-1-2-21111110220-2-2-211111122-1-1-1-1-1-1-1-1-2-200220000020-20011-1-1000-1-100001100000
χ402222-122-2-2-1222-1222-1-1-12-1-1-122-12-1-1-2-2-2-2111111-2-21111-1-1-1-1-2-211111102-202-2-21111-1-122-1-111-1-1-1-12200-2-200000-20200-1-111000110000-1-100000
χ4122-2-222200-2-22-2-2-2-222222-2-2-2-22-2-22200000000002-222-2-22-2-2200000000000002-222-2-2000000000000002i−2i000000000000000000000002i−2i002i−2i000
χ4222-2-222200-2-22-2-2-2-222222-2-2-2-22-2-22200000000002-222-2-22-2-2200000000000002-222-2-200000000000000−2i2i00000000000000000000000−2i2i00−2i2i000
χ4322-2-222200-2-22-2-2-2-222222-2-2-2-22-2-2220000000000-22-2-2222-2-220000000000000-22-2-222000000000000002i−2i000000000000000000000002i−2i00−2i2i000
χ4422-2-222200-2-22-2-2-2-222222-2-2-2-22-2-2220000000000-22-2-2222-2-220000000000000-22-2-22200000000000000−2i2i00000000000000000000000−2i2i002i−2i000
χ452-2-222222i−2i-2-2-2222-2-2-2222-22-22-22-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i00000022-2-22i−2i2i−2i2i2i−2i−2i000000000000000000000002i−2i002-2000000000000000002-200002i−2i00000
χ462-2-222222i−2i-2-2-2222-2-2-2222-22-22-22-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i00000022-2-22i−2i2i−2i2i2i−2i−2i00000000000000000000000−2i2i00-2200000000000000000-220000−2i2i00000
χ472-2-22222−2i2i-2-2-2222-2-2-2222-22-22-22-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i00000022-2-2−2i2i−2i2i−2i−2i2i2i000000000000000000000002i−2i00-2200000000000000000-2200002i−2i00000
χ482-2-22222−2i2i-2-2-2222-2-2-2222-22-22-22-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i00000022-2-2−2i2i−2i2i−2i−2i2i2i00000000000000000000000−2i2i002-2000000000000000002-20000−2i2i00000
χ492-2-22-1222i−2i1-2-22-12-2-21-1-121-112-2-1-2112i−2i2i−2i−ii−i−iii00−i3i3−i3i3-1-1112i−2i−ii−i−iii0000000−i3i3−i3i3−i3i3003−33−333−3−32i−2i002-20000000000−i3i33−3000-110000−ii00000
χ502-2-22-1222i−2i1-2-22-12-2-21-1-121-112-2-1-2112i−2i2i−2i−ii−i−iii00−i3i3−i3i3-1-1112i−2i−ii−i−iii0000000−i3i3−i3i3i3−i3003−3−3333−3−3−2i2i00-220000000000i3−i3−330001-10000i−i00000
χ512-2-22-1222i−2i1-2-22-12-2-21-1-121-112-2-1-2112i−2i2i−2i−ii−i−iii00i3−i3i3−i3-1-1112i−2i−ii−i−iii0000000i3−i3i3−i3−i3i300−333−3−3−333−2i2i00-220000000000−i3i33−30001-10000i−i00000
χ522-2-22-1222i−2i1-2-22-12-2-21-1-121-112-2-1-2112i−2i2i−2i−ii−i−iii00i3−i3i3−i3-1-1112i−2i−ii−i−iii0000000i3−i3i3−i3i3−i300−33−33−3−3332i−2i002-20000000000i3−i3−33000-110000−ii00000
χ532-2-22-122−2i2i1-2-22-12-2-21-1-121-112-2-1-211−2i2i−2i2ii−iii−i−i00−i3i3−i3i3-1-111−2i2ii−iii−i−i0000000−i3i3−i3i3−i3i300−33−33−3−333−2i2i002-20000000000−i3i3−33000-110000i−i00000
χ542-2-22-122−2i2i1-2-22-12-2-21-1-121-112-2-1-211−2i2i−2i2ii−iii−i−i00−i3i3−i3i3-1-111−2i2ii−iii−i−i0000000−i3i3−i3i3i3−i300−333−3−3−3332i−2i00-220000000000i3−i33−30001-10000−ii00000
χ552-2-22-122−2i2i1-2-22-12-2-21-1-121-112-2-1-211−2i2i−2i2ii−iii−i−i00i3−i3i3−i3-1-111−2i2ii−iii−i−i0000000i3−i3i3−i3−i3i3003−3−3333−3−32i−2i00-220000000000−i3i3−330001-10000−ii00000
χ562-2-22-122−2i2i1-2-22-12-2-21-1-121-112-2-1-211−2i2i−2i2ii−iii−i−i00i3−i3i3−i3-1-111−2i2ii−iii−i−i0000000i3−i3i3−i3i3−i3003−33−333−3−3−2i2i002-20000000000i3−i33−3000-110000i−i00000
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χ864-44-4-24-200-2-2-422-4422-21-2-2-11222-22-10000003i−3i−3i3i00−2i32i32i3−2i31-11-100003i−3i−3i3i0000000i3−i3−i3i300−232300003−3−33000000000000000000000000000000000000
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χ904-4-4444-24i−4i-42-4-244-42-44-2-2-4-22-2242-424i−4i−2i2i4i−4i−2i−2i2i2i000000-2-222−2i2i4i−4i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000000
χ914-4-4444-2−4i4i-42-4-244-42-44-2-2-4-22-2242-42−4i4i2i−2i−4i4i2i2i−2i−2i000000-2-2222i−2i−4i4i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000000
χ924-4-444-244i−4i-4-4244-22-4-4-24-224-4-22-222-4−2i2i4i−4i4i−4i4i4i−4i−4i000000-2-222−2i2i−2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000000
χ934-4-444-24−4i4i-4-4244-22-4-4-24-224-4-22-222-42i−2i−4i4i−4i4i−4i−4i4i4i000000-2-2222i−2i2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000000
χ944-4-444-2-24i−4i-422-24-222-4-2-212-221-1-2-122−2i2i−2i2i4i−4i−2i−2i2i2i00000011-1-1i−i−2i2iii−i−i00000000000000000000000000000003-300003i−3i00000000000000000000
χ954-4-444-2-24i−4i-422-24-222-4-2-212-221-1-2-122−2i2i−2i2i4i−4i−2i−2i2i2i00000011-1-1i−i−2i2iii−i−i0000000000000000000000000000000-330000−3i3i00000000000000000000
χ964-4-444-2-2−4i4i-422-24-222-4-2-212-221-1-2-1222i−2i2i−2i−4i4i2i2i−2i−2i00000011-1-1−ii2i−2i−i−iii00000000000000000000000000000003-30000−3i3i00000000000000000000
χ974-4-444-2-2−4i4i-422-24-222-4-2-212-221-1-2-1222i−2i2i−2i−4i4i2i2i−2i−2i00000011-1-1−ii2i−2i−i−iii0000000000000000000000000000000-3300003i−3i00000000000000000000
χ984-4-44-24-24i−4i22-4-2-24-422-21-221-1-22-222-14i−4i−2i2i−2i2iii−i−i00−2i32i3−2i32i311-1-1−2i2i−2i2iii−i−i0000000i3−i3i3−i3000023−2300−3−333000000000000000000000000000000000000
χ994-4-44-24-24i−4i22-4-2-24-422-21-221-1-22-222-14i−4i−2i2i−2i2iii−i−i002i3−2i32i3−2i311-1-1−2i2i−2i2iii−i−i0000000−i3i3−i3i30000−23230033−3−3000000000000000000000000000000000000
χ1004-4-44-24-2−4i4i22-4-2-24-422-21-221-1-22-222-1−4i4i2i−2i2i−2i−i−iii00−2i32i3−2i32i311-1-12i−2i2i−2i−i−iii0000000i3−i3i3−i30000−23230033−3−3000000000000000000000000000000000000
χ1014-4-44-24-2−4i4i22-4-2-24-422-21-221-1-22-222-1−4i4i2i−2i2i−2i−i−iii002i3−2i32i3−2i311-1-12i−2i2i−2i−i−iii0000000−i3i3−i3i3000023−2300−3−333000000000000000000000000000000000000
χ1024-4-44-2-244i−4i2-424-2-22-421-2-2-1-22-2212-12−2i2i4i−4i−2i2i−2i−2i2i2i00000011-1-1−2i2ii−iii−i−i00000000000−2i32i3000023−2300000000000000000000i3−i3−330000000000000000
χ1034-4-44-2-244i−4i2-424-2-22-421-2-2-1-22-2212-12−2i2i4i−4i−2i2i−2i−2i2i2i00000011-1-1−2i2ii−iii−i−i000000000002i3−2i30000−232300000000000000000000−i3i33−30000000000000000
χ1044-4-44-2-24−4i4i2-424-2-22-421-2-2-1-22-2212-122i−2i−4i4i2i−2i2i2i−2i−2i00000011-1-12i−2i−ii−i−iii00000000000−2i32i30000−232300000000000000000000i3−i33−30000000000000000
χ1054-4-44-2-24−4i4i2-424-2-22-421-2-2-1-22-2212-122i−2i−4i4i2i−2i2i2i−2i−2i00000011-1-12i−2i−ii−i−iii000000000002i3−2i3000023−2300000000000000000000−i3i3−330000000000000000
χ1068888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-42222000000-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000000000000
χ1078888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-2-2-2-2000000-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000000000
χ10888-8-88-4-400-84-44-844-48-4-42444-224-2-4-400000000000000002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ10988-8-8-4-48004-8-4-84448-42-4-4-2444-4-242-400000000000000002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4-40044-44444-4-4222-2-2-2-22-2-2220000006-66-6000000-111-10000-33-3300000000000000000000000000000000000000000000000000000000000
χ11188-8-8-4-4-40044-44444-4-4222-2-2-2-22-2-222000000-66-66000000-111-100003-33-300000000000000000000000000000000000000000000000000000000000
χ1128-88-88-4-4008-444-84-44-8-4-42-44-4-2-2424400000000000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1138-88-8-4-4800-484-844-4-842-4-424-444-2-4-2400000000000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1148-88-8-4-4-400-4-44444-4442222-22-2-2-22-2-20000006i−6i−6i6i000000-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1158-88-8-4-4-400-4-44444-4442222-22-2-2-22-2-2000000−6i6i6i−6i000000-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-48i−8i444-4-4-4444222-22-22-22-2-2-2−4i4i−4i4i−4i4i2i2i−2i−2i000000-1-1112i−2i2i−2i−i−iii00000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-4−8i8i444-4-4-4444222-22-22-22-2-2-24i−4i4i−4i4i−4i−2i−2i2i2i000000-1-111−2i2i−2i2iii−i−i00000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).