Finite Group Databasebeta

← Group #11787808

Character table — Group #11787808

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222222222444444444444444444888888888888888888888812121212121212121212121212121212121212122424242424242424242424242424363636367272
order122222334444666666121212123666666612121212121212121212668812122424242424242424242424242424242422224444444412121212121212126666881212121224242424444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
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
χ5111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ6111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ7111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ8111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111111111-1-1
χ91-1-11-111111-1-1-1-111-1-111-1-11-11-1-1-111111-111-1-1-1-11-1i−i1-1ii−i−iiiiiii−i−i−i−i−i−i11-1-1ii−i−i11-1-11111-1-1-1-111-1-1i−iii−i−iii−i−iii−i−i1-1
χ101-1-11-111111-1-1-1-111-1-111-1-11-11-1-1-111111-111-1-1-1-11-1i−i1-1ii−i−iiiiiii−i−i−i−i−i−i11-1-1−i−iii-1-111-1-1-1-1111111-1-1i−i−i−iiiii−i−i−i−iii-11
χ111-1-11-111111-1-1-1-111-1-111-1-11-11-1-1-111111-111-1-1-1-11-1i−i1-1ii−i−iiiiiii−i−i−i−i−i−i-1-111ii−i−i11-1-11111-1-1-1-1-1-111−iiii−i−i−i−iii−i−iii-11
χ121-1-11-111111-1-1-1-111-1-111-1-11-11-1-1-111111-111-1-1-1-11-1i−i1-1ii−i−iiiiiii−i−i−i−i−i−i-1-111−i−iii-1-111-1-1-1-11111-1-111−ii−i−iii−i−iiiii−i−i1-1
χ131-1-11-111111-1-1-1-111-1-111-1-11-11-1-1-111111-111-1-1-1-11-1−ii1-1−i−iii−i−i−i−i−i−iiiiiii11-1-1ii−i−i-1-111-1-1-1-1111111-1-1−iiii−i−i−i−iiiii−i−i-11
χ141-1-11-111111-1-1-1-111-1-111-1-11-11-1-1-111111-111-1-1-1-11-1−ii1-1−i−iii−i−i−i−i−i−iiiiiii11-1-1−i−iii11-1-11111-1-1-1-111-1-1−ii−i−iii−i−iii−i−iii1-1
χ151-1-11-111111-1-1-1-111-1-111-1-11-11-1-1-111111-111-1-1-1-11-1−ii1-1−i−iii−i−i−i−i−i−iiiiiii-1-111ii−i−i-1-111-1-1-1-11111-1-111i−iii−i−iii−i−i−i−iii1-1
χ161-1-11-111111-1-1-1-111-1-111-1-11-11-1-1-111111-111-1-1-1-11-1−ii1-1−i−iii−i−i−i−i−i−iiiiiii-1-111−i−iii11-1-11111-1-1-1-1-1-111i−i−i−iiiii−i−iii−i−i-11
χ1722222222-2-2-2-2222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-22200-2-200000000000000002-22-200000000000000002-22-20000000000000000
χ1822222222-2-2-2-2222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-22200-2-20000000000000000-22-220000000000000000-22-220000000000000000
χ192222222-12222-1-12-1222222-12-1-1-1-1-122-1-12-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-122220000000000000000-1-1-1-1220000-1-1-1-1000000
χ202222222-12222-1-12-1222222-12-1-1-1-1-122-1-12-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000000000001111-2-200001111000000
χ212222222-12222-1-12-1222222-12-1-1-1-1-122-1-12-1-1-1-1-1-1-1-1-2-2-1-1-2-2-2-211111111111122220000000000000000-1-1-1-1-2-200001111000000
χ222222222-12222-1-12-1222222-12-1-1-1-1-122-1-12-1-1-1-1-1-1-1-1-2-2-1-1-2-2-2-2111111111111-2-2-2-200000000000000001111220000-1-1-1-1000000
χ232222222-1-2-2-2-2-1-12-122-2-2-2-2-12-1-1-1-1-12-211-2111111-1-100110000333−3−3−3333−3−3−32-22-20000000000000000-11-110000003−33−3000000
χ242222222-1-2-2-2-2-1-12-122-2-2-2-2-12-1-1-1-1-12-211-2111111-1-100110000333−3−3−3333−3−3−3-22-2200000000000000001-11-1000000−33−33000000
χ252222222-1-2-2-2-2-1-12-122-2-2-2-2-12-1-1-1-1-12-211-2111111-1-100110000−3−3−3333−3−3−33332-22-20000000000000000-11-11000000−33−33000000
χ262222222-1-2-2-2-2-1-12-122-2-2-2-2-12-1-1-1-1-12-211-2111111-1-100110000−3−3−3333−3−3−3333-22-2200000000000000001-11-10000003−33−3000000
χ27222222-12222222-12-1-1-1-1-1-1-1-122-1-1-1-1-122-1-1-12-1-12-1-122-1-1-1-1-1-12-1-12-1-12-1-12-1-1000022222222-1-1-1-1-1-1-1-1000000-1-1-1-10000000000
χ28222222-12222222-12-1-1-1-1-1-1-1-122-1-1-1-1-122-1-1-12-1-12-1-122-1-1-1-1-1-12-1-12-1-12-1-12-1-10000-2-2-2-2-2-2-2-21111111100000011110000000000
χ29222222-12222222-12-1-1-1-1-1-1-1-122-1-1-1-1-122-1-1-12-1-12-1-1-2-2-1-11111-211-211-211-21100002222-2-2-2-211111111000000-1-1-1-10000000000
χ30222222-12222222-12-1-1-1-1-1-1-1-122-1-1-1-1-122-1-1-12-1-12-1-1-2-2-1-11111-211-211-211-2110000-2-2-2-22222-1-1-1-1-1-1-1-100000011110000000000
χ312222-2-2222-22-222222222222-2-2-2222-2-22-2-222222-2-2-200-2-2000000000000000000000000000000000000000000000000002-22-200
χ322222-2-2222-22-222222222222-2-2-2222-2-22-2-222222-2-2-200-2-200000000000000000000000000000000000000000000000000-22-2200
χ332222-2-222-22-22222222-2-2-2-22-2-2-2222-22-222-2-2-2-2-22-2-20022000000000000000000002-22-20000000000000000002-22-20000000000
χ342222-2-222-22-22222222-2-2-2-22-2-2-2222-22-222-2-2-2-2-22-2-2002200000000000000000000-22-22000000000000000000-22-220000000000
χ352222-2-2-12-22-2222-12-1-11111-11-2-2-1-1-11-1-22-111-21121100-1-13−33−303−303−303−303−300002-22-2000033−3−333−3−3000000-11-110000000000
χ362222-2-2-12-22-2222-12-1-11111-11-2-2-1-1-11-1-22-111-21121100-1-13−33−303−303−303−303−30000-22-220000−3−333−3−3330000001-11-10000000000
χ372222-2-2-12-22-2222-12-1-11111-11-2-2-1-1-11-1-22-111-21121100-1-1−33−330−330−330−330−3300002-22-20000−3−333−3−333000000-11-110000000000
χ382222-2-2-12-22-2222-12-1-11111-11-2-2-1-1-11-1-22-111-21121100-1-1−33−330−330−330−330−330000-22-22000033−3−333−3−30000001-11-10000000000
χ392-2-222-2222-2-22-2-222-2-222-2-222-22-2-22-2-22-2222-2-2-22-2200-22000000000000000000000000000000000000000000000000002i−2i−2i2i00
χ402-2-222-2222-2-22-2-222-2-222-2-222-22-2-22-2-22-2222-2-2-22-2200-2200000000000000000000000000000000000000000000000000−2i2i2i−2i00
χ412-2-222-222-222-2-2-222-2-2-2-22222-22-2-22-22-22-2-2-2222-2-22002-2000000000000000000002i−2i−2i2i0000000000000000002i−2i−2i2i0000000000
χ422-2-222-222-222-2-2-222-2-2-2-22222-22-2-22-22-22-2-2-2222-2-22002-200000000000000000000−2i2i2i−2i000000000000000000−2i2i2i−2i0000000000
χ432-2-222-2-12-222-2-2-2-121111-1-1-1-1-2211-11-1-221112-1-1-21-100-11−i3i3i3−i30−i3i30−i3i30i3−i30i3−i300002i−2i−2i2i0000−3−33333−3−3000000−iii−i0000000000
χ442-2-222-2-12-222-2-2-2-121111-1-1-1-1-2211-11-1-221112-1-1-21-100-11−i3i3i3−i30−i3i30−i3i30i3−i30i3−i30000−2i2i2i−2i000033−3−3−3−333000000i−i−ii0000000000
χ452-2-222-2-12-222-2-2-2-121111-1-1-1-1-2211-11-1-221112-1-1-21-100-11i3−i3−i3i30i3−i30i3−i30−i3i30−i3i300002i−2i−2i2i000033−3−3−3−333000000−iii−i0000000000
χ462-2-222-2-12-222-2-2-2-121111-1-1-1-1-2211-11-1-221112-1-1-21-100-11i3−i3−i3i30i3−i30i3−i30−i3i30−i3i30000−2i2i2i−2i0000−3−33333−3−3000000i−i−ii0000000000
χ472-2-22-2222-2-222-2-222-2-2-2-2222-22-2-2-222-2-2-22-2-222222-200-2200000000000000002-2-2200000000000000002-2-220000000000000000
χ482-2-22-2222-2-222-2-222-2-2-2-2222-22-2-2-222-2-2-22-2-222222-200-220000000000000000-222-20000000000000000-222-20000000000000000
χ492-2-22-222-122-2-2112-1-2-222-2-2-1-2-1111-122-1-1-2-1-11111-112i−2i-112i2i−2i−2i−i−i−i−i−i−iiiiiii22-2-20000000000000000-1-1112i−2i0000−i−iii000000
χ502-2-22-222-122-2-2112-1-2-222-2-2-1-2-1111-122-1-1-2-1-11111-112i−2i-112i2i−2i−2i−i−i−i−i−i−iiiiiii-2-222000000000000000011-1-1−2i2i0000ii−i−i000000
χ512-2-22-222-122-2-2112-1-2-222-2-2-1-2-1111-122-1-1-2-1-11111-11−2i2i-11−2i−2i2i2iiiiiii−i−i−i−i−i−i22-2-20000000000000000-1-111−2i2i0000ii−i−i000000
χ522-2-22-222-122-2-2112-1-2-222-2-2-1-2-1111-122-1-1-2-1-11111-11−2i2i-11−2i−2i2i2iiiiiii−i−i−i−i−i−i-2-222000000000000000011-1-12i−2i0000−i−iii000000
χ532-2-22-222-1-2-222112-1-2-2-2-222-1-2-1111-12-211211-1-1-1-1-11001-10000−i3−i3−i3i3i3i3i3i3i3−i3−i3−i32-2-220000000000000000-111-1000000−i3i3i3−i3000000
χ542-2-22-222-1-2-222112-1-2-2-2-222-1-2-1111-12-211211-1-1-1-1-11001-10000−i3−i3−i3i3i3i3i3i3i3−i3−i3−i3-222-200000000000000001-1-11000000i3−i3−i3i3000000
χ552-2-22-222-1-2-222112-1-2-2-2-222-1-2-1111-12-211211-1-1-1-1-11001-10000i3i3i3−i3−i3−i3−i3−i3−i3i3i3i32-2-220000000000000000-111-1000000i3−i3−i3i3000000
χ562-2-22-222-1-2-222112-1-2-2-2-222-1-2-1111-12-211211-1-1-1-1-11001-10000i3i3i3−i3−i3−i3−i3−i3−i3i3i3i3-222-200000000000000001-1-11000000−i3i3i3−i3000000
χ572-2-22-22-1222-2-2-2-2-1211-1-111-112-211-1-1-1221-1-1-211-2-112i−2i-11−i−iii2i−i−i2i−i−i−2iii−2iii00002i2i−2i−2i22-2-2-1-1-1-11111000000−i−iii0000000000
χ582-2-22-22-1222-2-2-2-2-1211-1-111-112-211-1-1-1221-1-1-211-2-112i−2i-11−i−iii2i−i−i2i−i−i−2iii−2iii0000−2i−2i2i2i-2-2221111-1-1-1-1000000ii−i−i0000000000
χ592-2-22-22-1222-2-2-2-2-1211-1-111-112-211-1-1-1221-1-1-211-2-11−2i2i-11ii−i−i−2iii−2iii2i−i−i2i−i−i00002i2i−2i−2i-2-2221111-1-1-1-1000000−i−iii0000000000
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χ874-4-444-4-244-4-44-4-4-2422-2-222-2-2-4422-2224-4-2-2-2-42242-2002-200000000000000000000000000000000000000000000000000000000
χ884-4-444-4-2-24-4-4422-2-222-2-2221-22-2-1-1122-22-2112-1-1-2-1100-11000003i−3i0−3i3i0−3i3i03i−3i0000000000000000000000000000000000000000
χ894-4-444-4-2-24-4-4422-2-222-2-2221-22-2-1-1122-22-2112-1-1-2-1100-1100000−3i3i03i−3i03i−3i0−3i3i0000000000000000000000000000000000000000
χ904-4-444-4-2-2-444-422-2-22222-2-21-22-2-1-112-22-22-1-1-2112-11001-1−2i32i32i3−2i30i3−i30i3−i30−i3i30−i3i30000000000000000000000000000000000000000
χ914-4-444-4-2-2-444-422-2-22222-2-21-22-2-1-112-22-22-1-1-2112-11001-12i3−2i3−2i32i30−i3i30−i3i30i3−i30i3−i30000000000000000000000000000000000000000
χ924-4-44-44-24-4-444-4-4-242222-2-2-224-422-2-22-4-4-2224-2-24-22002-200000000000000000000000000000000000000000000000000000000
χ934-4-44-44-2-244-4-422-2-222-2-22212-22-1-11-2-2-2-22112-1-121-14i−4i1-1−2i−2i2i2i−2iii−2iii2i−i−i2i−i−i0000000000000000000000000000000000000000
χ944-4-44-44-2-244-4-422-2-222-2-22212-22-1-11-2-2-2-22112-1-121-1−4i4i1-12i2i−2i−2i2i−i−i2i−i−i−2iii−2iii0000000000000000000000000000000000000000
χ954-4-44-44-2-2-4-44422-2-22222-2-212-22-1-11-2222-2-1-1-211-21-100-110000−2i3i3i32i3−i3−i32i3−i3−i3−2i3i3i30000000000000000000000000000000000000000
χ964-4-44-44-2-2-4-44422-2-22222-2-212-22-1-11-2222-2-1-1-211-21-100-1100002i3−i3−i3−2i3i3i3−2i3i3i32i3−i3−i30000000000000000000000000000000000000000
χ9788-8-8008-40000-44-848-80000-4000-4440000000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-800-4-40000-4444-4443−4343−4320002-2-200000−23230−2323000000000000000000000000000000000000000000000000000000000000000
χ9988-8-800-4-40000-4444-44−4343−434320002-2-20000023−23023−23000000000000000000000000000000000000000000000000000000000000000
χ1008-88-8008-400004-4-84-880000-40004-440000000000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-800-4-400004-4444-443−43−43432000-22-200000−2323023−23000000000000000000000000000000000000000000000000000000000000000
χ1028-88-800-4-400004-4444-4−434343−432000-22-20000023−230−2323000000000000000000000000000000000000000000000000000000000000000

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