Finite Group Databasebeta

← Group #11787681

Character table — Group #11787681

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222222222444444444444444444888888888888888888888812121212121212121212121212121212121212122424242424242424242424242424363636367272
order12222233444466666612121212366666661212121212121212121266881212242424242424242424242424242424242244444444441212121212121212668812121212121224242424444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1
χ6111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ7111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ8111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-111111111-1-1
χ91-1-111-1111-1-11-1-1-111-111-1-111-11-1-11-11-11-111-1-1-111-1i−i1-1ii−i−iiiiiii−i−i−i−i−i−i1-1ii−i−i1-1ii−i−iiiii−i−i−i−i1-11-11-1ii−i−i11-1-1i−ii−i1-1
χ101-1-111-1111-1-11-1-1-111-111-1-111-11-1-11-11-11-111-1-1-111-1i−i1-1ii−i−iiiiiii−i−i−i−i−i−i1-1−i−iii1-1ii−i−iiiii−i−i−i−i1-1-111-1−i−iii-1-111−ii−ii-11
χ111-1-111-1111-1-11-1-1-111-111-1-111-11-1-11-11-11-111-1-1-111-1i−i1-1ii−i−iiiiiii−i−i−i−i−i−i-11ii−i−i-11−i−iii−i−i−i−iiiii-111-1-11ii−i−i11-1-1−ii−ii-11
χ121-1-111-1111-1-11-1-1-111-111-1-111-11-1-11-11-11-111-1-1-111-1i−i1-1ii−i−iiiiiii−i−i−i−i−i−i-11−i−iii-11−i−iii−i−i−i−iiiii-11-11-11−i−iii-1-111i−ii−i1-1
χ131-1-111-1111-1-11-1-1-111-111-1-111-11-1-11-11-11-111-1-1-111-1−ii1-1−i−iii−i−i−i−i−i−iiiiiii1-1ii−i−i1-1−i−iii−i−i−i−iiiii1-1-111-1ii−i−i-1-111i−ii−i-11
χ141-1-111-1111-1-11-1-1-111-111-1-111-11-1-11-11-11-111-1-1-111-1−ii1-1−i−iii−i−i−i−i−i−iiiiiii1-1−i−iii1-1−i−iii−i−i−i−iiiii1-11-11-1−i−iii11-1-1−ii−ii1-1
χ151-1-111-1111-1-11-1-1-111-111-1-111-11-1-11-11-11-111-1-1-111-1−ii1-1−i−iii−i−i−i−i−i−iiiiiii-11ii−i−i-11ii−i−iiiii−i−i−i−i-11-11-11ii−i−i-1-111−ii−ii1-1
χ161-1-111-1111-1-11-1-1-111-111-1-111-11-1-11-11-11-111-1-1-111-1−ii1-1−i−iii−i−i−i−i−i−iiiiiii-11−i−iii-11ii−i−iiiii−i−i−i−i-111-1-11−i−iii11-1-1i−ii−i-11
χ1722222222-2-2-2-2222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-22200-2-20000000000000000002-22-2000000000000000000002-22-20000000000
χ1822222222-2-2-2-2222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-22200-2-2000000000000000000-22-2200000000000000000000-22-220000000000
χ192222222-122222-1-12-12-1-1-1-1-122-1-1-1-1-122-1-1-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1220000222222-1-1-1-1-1-1-1-1-1-100-1-100000000000000
χ202222222-122222-1-12-12-1-1-1-1-122-1-1-1-1-122-1-1-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-20000-2-2-2-2-2-21111111111001100000000000000
χ212222222-122222-1-12-12-1-1-1-1-122-1-1-1-1-122-1-1-1-12-1-12-1-1-2-2-1-11111-2-21111-2-2111122000022-2-2-2-211111111-1-100-1-100000000000000
χ222222222-122222-1-12-12-1-1-1-1-122-1-1-1-1-122-1-1-1-12-1-12-1-1-2-2-1-11111-2-21111-2-21111-2-20000-2-22222-1-1-1-1-1-1-1-111001100000000000000
χ23222222-122222-122-12-12222-1-1-12-1-1-12-1-122-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-100222200000000000000002200-1-1-1-1-1-1-1-1000000
χ24222222-122222-122-12-12222-1-1-12-1-1-12-1-122-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-20000000000000000-2-20011111111000000
χ25222222-122222-122-12-12222-1-1-12-1-1-12-1-122-1-1-1-1-1-1-1-1-2-2-1-1-2-2-2-21111111111110022220000000000000000-2-200-1-1-1-11111000000
χ26222222-122222-122-12-12222-1-1-12-1-1-12-1-122-1-1-1-1-1-1-1-1-2-2-1-1-2-2-2-211111111111100-2-2-2-2000000000000000022001111-1-1-1-1000000
χ27222222-12-2-2-2-2-122-12-1-2-2-2-2-1-1-12-1-1-1211-2-2111111-1-1001100003−333−3−33−333−3−3002-22-200000000000000000000-11-113−33−3000000
χ28222222-12-2-2-2-2-122-12-1-2-2-2-2-1-1-12-1-1-1211-2-2111111-1-1001100003−333−3−33−333−3−300-22-22000000000000000000001-11-1−33−33000000
χ29222222-12-2-2-2-2-122-12-1-2-2-2-2-1-1-12-1-1-1211-2-2111111-1-100110000−33−3−333−33−3−333002-22-200000000000000000000-11-11−33−33000000
χ30222222-12-2-2-2-2-122-12-1-2-2-2-2-1-1-12-1-1-1211-2-2111111-1-100110000−33−3−333−33−3−33300-22-22000000000000000000001-11-13−33−3000000
χ312222-2-2222-22-222222222222-2-2-2222-22-2-2-222222-2-2-200-2-20000000000000000000000000000000000000000000000000022-2-200
χ322222-2-2222-22-222222222222-2-2-2222-22-2-2-222222-2-2-200-2-200000000000000000000000000000000000000000000000000-2-22200
χ332222-2-222-22-22222222-2-2-2-22-2-2-2222-2-2222-2-2-2-2-22-2-200220000000000000000220000-2-20000000000002200-2-200000000000000
χ342222-2-222-22-22222222-2-2-2-22-2-2-2222-2-2222-2-2-2-2-22-2-200220000000000000000-2-2000022000000000000-2-2002200000000000000
χ352222-2-22-1-22-222-1-12-121111-1-2-21-1-1-11-22-1-111-21121100-1-13−33−3003−33−3003−33−3220000-2-2000033−3−333−3−3-1-1001100000000000000
χ362222-2-22-1-22-222-1-12-121111-1-2-21-1-1-11-22-1-111-21121100-1-13−33−3003−33−3003−33−3-2-20000220000−3−333−3−3331100-1-100000000000000
χ372222-2-22-1-22-222-1-12-121111-1-2-21-1-1-11-22-1-111-21121100-1-1−33−3300−33−3300−33−33220000-2-20000−3−333−3−333-1-1001100000000000000
χ382222-2-22-1-22-222-1-12-121111-1-2-21-1-1-11-22-1-111-21121100-1-1−33−3300−33−3300−33−33-2-2000022000033−3−333−3−31100-1-100000000000000
χ392-2-222-222-222-2-2-2-222-2-2-22222-22-2-22-2-22-22-2-2222-22-200-220000000000000000002i−2i−2i2i000000000000000000002i−2i−2i2i0000000000
χ402-2-222-222-222-2-2-2-222-2-2-22222-22-2-22-2-22-22-2-2222-22-200-22000000000000000000−2i2i2i−2i00000000000000000000−2i2i2i−2i0000000000
χ412-2-222-22-12-2-22-2112-1-2-1-111-12-2-111-112-2-11-1-1-2112-112i−2i-11−i−iii2i2i−i−i−i−i−2i−2iiiii2-200002-22i2i−2i−2i−i−i−i−iiiii-1100-1100000000000000
χ422-2-222-22-12-2-22-2112-1-2-1-111-12-2-111-112-2-11-1-1-2112-112i−2i-11−i−iii2i2i−i−i−i−i−2i−2iiiii-220000-22−2i−2i2i2iiiii−i−i−i−i1-1001-100000000000000
χ432-2-222-22-12-2-22-2112-1-2-1-111-12-2-111-112-2-11-1-1-2112-11−2i2i-11ii−i−i−2i−2iiiii2i2i−i−i−i−i2-200002-2−2i−2i2i2iiiii−i−i−i−i-1100-1100000000000000
χ442-2-222-22-12-2-22-2112-1-2-1-111-12-2-111-112-2-11-1-1-2112-11−2i2i-11ii−i−i−2i−2iiiii2i2i−i−i−i−i-220000-222i2i−2i−2i−i−i−i−iiiii1-1001-100000000000000
χ452-2-222-2-122-2-221-2-2-12122-2-2-1-11211-1-2-112-2-1-1111-1-112i−2i-112i2i−2i−2i−i−i−i−i−i−iiiiiii002i2i−2i−2i00000000000000002-200−i−iii-1-111000000
χ462-2-222-2-122-2-221-2-2-12122-2-2-1-11211-1-2-112-2-1-1111-1-112i−2i-112i2i−2i−2i−i−i−i−i−i−iiiiiii00−2i−2i2i2i0000000000000000-2200ii−i−i11-1-1000000
χ472-2-222-2-122-2-221-2-2-12122-2-2-1-11211-1-2-112-2-1-1111-1-11−2i2i-11−2i−2i2i2iiiiiii−i−i−i−i−i−i002i2i−2i−2i0000000000000000-2200−i−iii11-1-1000000
χ482-2-222-2-122-2-221-2-2-12122-2-2-1-11211-1-2-112-2-1-1111-1-11−2i2i-11−2i−2i2i2iiiiiii−i−i−i−i−i−i00−2i−2i2i2i00000000000000002-200ii−i−i-1-111000000
χ492-2-222-2-12-222-21-2-2-121-2-222-1-11211-1-21-1-2211-1-1-11-11001-10000−i3i3−i3−i3i3i3i3−i3i3i3−i3−i3002i−2i−2i2i00000000000000000000−iii−i−333−3000000
χ502-2-222-2-12-222-21-2-2-121-2-222-1-11211-1-21-1-2211-1-1-11-11001-10000−i3i3−i3−i3i3i3i3−i3i3i3−i3−i300−2i2i2i−2i00000000000000000000i−i−ii3−3−33000000
χ512-2-222-2-12-222-21-2-2-121-2-222-1-11211-1-21-1-2211-1-1-11-11001-10000i3−i3i3i3−i3−i3−i3i3−i3−i3i3i3002i−2i−2i2i00000000000000000000−iii−i3−3−33000000
χ522-2-222-2-12-222-21-2-2-121-2-222-1-11211-1-21-1-2211-1-1-11-11001-10000i3−i3i3i3−i3−i3−i3i3−i3−i3i3i300−2i2i2i−2i00000000000000000000i−i−ii−333−3000000
χ532-2-22-222222-2-2-2-2-222-222-2-22-22-2-2-22222-2222-2-2-2-2-2200-22000000000000000000000000000000000000000000000000002i−2i−2i2i00
χ542-2-22-222222-2-2-2-2-222-222-2-22-22-2-2-22222-2222-2-2-2-2-2200-2200000000000000000000000000000000000000000000000000−2i2i2i−2i00
χ552-2-22-2222-2-222-2-2-222-2-2-2222-22-2-2-222-2-22-2-2-22222-22002-200000000000000002-20000-220000000000002-200-2200000000000000
χ562-2-22-2222-2-222-2-2-222-2-2-2222-22-2-2-222-2-22-2-2-22222-22002-20000000000000000-2200002-2000000000000-22002-200000000000000
χ572-2-22-222-1-2-222-2112-1-211-1-1-1-22111-1-1-2-2-11112-1-121-100-11−i3i3i3−i300−i3i3−i3i300i3−i3i3−i32-20000-220000−i3−i3i3i3i3i3−i3−i3-11001-100000000000000
χ582-2-22-222-1-2-222-2112-1-211-1-1-1-22111-1-1-2-2-11112-1-121-100-11−i3i3i3−i300−i3i3−i3i300i3−i3i3−i3-2200002-20000i3i3−i3−i3−i3−i3i3i31-100-1100000000000000
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χ904-4-44-444-244-4-4-4224-2-4-2-222-2-44222-2-2442-2-2-2-422-42-2002-200000000000000000000000000000000000000000000000000000000
χ914-4-44-44-2444-4-42-4-4-24244-4-4-22-2-422-24-2-2-44-2-222222-2002-200000000000000000000000000000000000000000000000000000000
χ924-4-44-44-24-4-4442-4-4-242-4-444-22-2-422-24224-422-2-2-2-22-200-2200000000000000000000000000000000000000000000000000000000
χ934-4-44-44-2-244-4-4222-2-22-2-22212-22-1-11-2-2-22-2112-1-12-1100-110000003i−3i−3i3i00−3i3i3i−3i0000000000000000000000000000000000000000
χ944-4-44-44-2-244-4-4222-2-22-2-22212-22-1-11-2-2-22-2112-1-12-1100-11000000−3i3i3i−3i003i−3i−3i3i0000000000000000000000000000000000000000
χ954-4-44-44-2-2-4-444222-2-2222-2-212-22-1-11-222-22-1-1-211-2-11001-1−2i32i32i3−2i300i3−i3i3−i300−i3i3−i3i30000000000000000000000000000000000000000
χ964-4-44-44-2-2-4-444222-2-2222-2-212-22-1-11-222-22-1-1-211-2-11001-12i3−2i3−2i32i300−i3i3−i3i300i3−i3i3−i30000000000000000000000000000000000000000
χ9788-8-800-480000-48-84-840000-4000-4440000000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-800-4-40000-4-4444443−4343−4320002-2-200000−23230−2323000000000000000000000000000000000000000000000000000000000000000
χ9988-8-800-4-40000-4-44444−4343−434320002-2-20000023−23023−23000000000000000000000000000000000000000000000000000000000000000
χ1008-88-800-4800004-884-8-40000-40004-440000000000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-800-4-4000044-444-443−43−43432000-22-200000−2323023−23000000000000000000000000000000000000000000000000000000000000000
χ1028-88-800-4-4000044-444-4−434343−432000-22-20000023−230−2323000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.