Finite Group Databasebeta

← Group #11787653

Character table — Group #11787653

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222222222444444444444444444888888888888888888888812121212121212121212121212121212121212122424242424242424242424242424363636367272
order1244222334446666121212121212366666666121212121212121212668812122424242424242424242424242424242422448888888824242424242424242466661212121224242424888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
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
χ5111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1
χ6111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-111
χ7111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-111
χ8111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-111-1-1-1-11111-1-1
χ911-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-1111-1-1-1111-11-11-11-111-1-1111111-1-1-1-1-1-11-11-1ii−i−iii−i−iiiii−i−i−i−i1-11-1111-1-1-1ii−i−iii−i−ii−i
χ1011-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-1111-1-1-1111-11-11-11-111-1-1111111-1-1-1-1-1-11-11-1−i−iii−i−iii−i−i−i−iiiii1-11-1111-1-1-1−i−iii−i−iii−ii
χ1111-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-1111-1-1-1111-11-11-11-111-1-1111111-1-1-1-1-1-1-11-11ii−i−iii−i−iiiii−i−i−i−i-11-11-1-1-1111ii−i−i−i−iii−ii
χ1211-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-1111-1-1-1111-11-11-11-111-1-1111111-1-1-1-1-1-1-11-11−i−iii−i−iii−i−i−i−iiiii-11-11-1-1-1111−i−iiiii−i−ii−i
χ1311-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-1111-1-1-1111-11-1-111-1-1-111-1-1-1-1-1-11111111-11-1ii−i−i−i−iii−i−i−i−iiiii-111-1-1-11-111ii−i−iii−i−i−ii
χ1411-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-1111-1-1-1111-11-1-111-1-1-111-1-1-1-1-1-11111111-11-1−i−iiiii−i−iiiii−i−i−i−i-111-1-1-11-111−i−iii−i−iiii−i
χ1511-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-1111-1-1-1111-11-1-111-1-1-111-1-1-1-1-1-1111111-11-11ii−i−i−i−iii−i−i−i−iiiii1-1-1111-11-1-1ii−i−i−i−iiii−i
χ1611-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-1111-1-1-1111-11-1-111-1-1-111-1-1-1-1-1-1111111-11-11−i−iiiii−i−iiiii−i−i−i−i1-1-1111-11-1-1−i−iiiii−i−i−ii
χ1722222222-1222222-1-1-12222-122-1-1-1-1-1-12-1-1-1-1-1-1-12-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222000000000000000022-1-1-1-1-1-1-1-10000000000
χ1822222222-1222222-1-1-12222-122-1-1-1-1-1-12-1-1-1-1-1-1-12-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000000000000-2-2111111110000000000
χ1922222222-1222222-1-1-12222-122-1-1-1-1-1-12-1-1-1-1-1-1-12-1-1-2-2-1-1-2-2-2-211111111111122220000000000000000-2-2-1-111-1-1110000000000
χ2022222222-1222222-1-1-12222-122-1-1-1-1-1-12-1-1-1-1-1-1-12-1-1-2-2-1-1-2-2-2-2111111111111-2-2-2-200000000000000002211-1-111-1-10000000000
χ212222222-12222-1-1-1222-1-1-1-1-1-1-1222-1-1-1-122-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1000022222222-1-1-1-1-1-1-1-10000000000-1-1-1-1000000
χ222222222-12222-1-1-1222-1-1-1-1-1-1-1222-1-1-1-122-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-10000-2-2-2-2-2-2-2-21111111100000000001111000000
χ232222222-12222-1-1-1222-1-1-1-1-1-1-1222-1-1-1-122-1-12-1-1-1-1-1-2-2-1-11111-2-21111-2-2111100002222-2-2-2-2111111110000000000-1-1-1-1000000
χ242222222-12222-1-1-1222-1-1-1-1-1-1-1222-1-1-1-122-1-12-1-1-1-1-1-2-2-1-11111-2-21111-2-211110000-2-2-2-22222-1-1-1-1-1-1-1-100000000001111000000
χ2522222-2-222-2-22-2-22222-2-22222-22-2-2-2-22-2-2222-2-2-222-200-22000000000000000000000000000000000000000000000000002-22-200
χ2622222-2-222-2-22-2-22222-2-22222-22-2-2-2-22-2-2222-2-2-222-200-2200000000000000000000000000000000000000000000000000-22-2200
χ272222-22-222-22-222222222222-2-2-22-2222-2-2-222222-2-2-200-2-200000000000000002-2-220000000000000000002-200-22000000000000
χ282222-22-222-22-222222222222-2-2-22-2222-2-2-222222-2-2-200-2-20000000000000000-222-2000000000000000000-22002-2000000000000
χ292222-22-22-1-22-2222-1-1-12222-1-2-21-11-1-1-1-211-1-1-1-1-1-21100110000−i3i3−i3−i3i3i3−i3i3−i3−i3i3i32-2-22000000000000000000-11−i3i31-1−i3i30000000000
χ302222-22-22-1-22-2222-1-1-12222-1-2-21-11-1-1-1-211-1-1-1-1-1-21100110000−i3i3−i3−i3i3i3−i3i3−i3−i3i3i3-222-20000000000000000001-1i3−i3-11i3−i30000000000
χ312222-22-22-1-22-2222-1-1-12222-1-2-21-11-1-1-1-211-1-1-1-1-1-21100110000i3−i3i3i3−i3−i3i3−i3i3i3−i3−i32-2-22000000000000000000-11i3−i31-1i3−i30000000000
χ322222-22-22-1-22-2222-1-1-12222-1-2-21-11-1-1-1-211-1-1-1-1-1-21100110000i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3-222-20000000000000000001-1−i3i3-11−i3i30000000000
χ332222-2-22222-2-2-2-22222-2-2222-22-2-22-2-2222-222-2-2-2-2-22002-2000000000000000000002-22-200000000000000000000002-22-2000000
χ342222-2-22222-2-2-2-22222-2-2222-22-2-22-2-2222-222-2-2-2-2-22002-200000000000000000000-22-220000000000000000000000-22-22000000
χ352222-2-22-122-2-211-122211-1-1-11-1-2-2211-1-12-2-1-1-21111-100-113−33−3003−33−3003−33−300002-22-2000033−3−333−3−30000000000-11-11000000
χ362222-2-22-122-2-211-122211-1-1-11-1-2-2211-1-12-2-1-1-21111-100-113−33−3003−33−3003−33−30000-22-220000−3−333−3−33300000000001-11-1000000
χ372222-2-22-122-2-211-122211-1-1-11-1-2-2211-1-12-2-1-1-21111-100-11−33−3300−33−3300−33−3300002-22-20000−3−333−3−3330000000000-11-11000000
χ382222-2-22-122-2-211-122211-1-1-11-1-2-2211-1-12-2-1-1-21111-100-11−33−3300−33−3300−33−330000-22-22000033−3−333−3−300000000001-11-1000000
χ3922-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22200-2-2000000000000000000000000000000000000000000000000002i−2i−2i2i00
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χ4122-2-22-2-22-122-2-2-22-11122-2-2-12-2-11111-12-1111-1-1-1-2-112-2-1122-2-2-1-1-1-1-1-11111112-22-200000000000000002-2-11-1-1-11110000000000
χ4222-2-22-2-22-122-2-2-22-11122-2-2-12-2-11111-12-1111-1-1-1-2-112-2-1122-2-2-1-1-1-1-1-1111111-22-220000000000000000-221-1111-1-1-10000000000
χ4322-2-22-2-22-122-2-2-22-11122-2-2-12-2-11111-12-1111-1-1-1-2-11-22-11-2-222111111-1-1-1-1-1-12-22-20000000000000000-22-1111-11-1-10000000000
χ4422-2-22-2-22-122-2-2-22-11122-2-2-12-2-11111-12-1111-1-1-1-2-11-22-11-2-222111111-1-1-1-1-1-1-22-2200000000000000002-21-1-1-11-1110000000000
χ4522-2-22-2-2-1222-211-12-2-2-1-111-1-112-2-211-1-12-2112-1-11-112-2-11-1-11122-1-1-1-1-2-2111100002i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii0000000000−i−iii000000
χ4622-2-22-2-2-1222-211-12-2-2-1-111-1-112-2-211-1-12-2112-1-11-112-2-11-1-11122-1-1-1-1-2-211110000−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i0000000000ii−i−i000000
χ4722-2-22-2-2-1222-211-12-2-2-1-111-1-112-2-211-1-12-2112-1-11-11-22-1111-1-1-2-2111122-1-1-1-100002i2i−2i−2i−2i−2i2i2iiiii−i−i−i−i0000000000−i−iii000000
χ4822-2-22-2-2-1222-211-12-2-2-1-111-1-112-2-211-1-12-2112-1-11-11-22-1111-1-1-2-2111122-1-1-1-10000−2i−2i2i2i2i2i−2i−2i−i−i−i−iiiii0000000000ii−i−i000000
χ4922-2-2-22-2222-222222-2-2-2-2-2-22-2-2-22-2222222-2-2-2-2-22-2-20022000000000000000000002i−2i−2i2i00000000000000000000002i−2i−2i2i000000
χ5022-2-2-22-2222-222222-2-2-2-2-2-22-2-2-22-2222222-2-2-2-2-22-2-2002200000000000000000000−2i2i2i−2i0000000000000000000000−2i2i2i−2i000000
χ5122-2-2-22-2-122-22-1-1-12-2-21111-111-22-2-1-1-1-12211-211-11100-1-13−3−33003−33−300−33−3300002i−2i−2i2i0000i3i3−i3−i3−i3−i3i3i30000000000−iii−i000000
χ5222-2-2-22-2-122-22-1-1-12-2-21111-111-22-2-1-1-1-12211-211-11100-1-13−3−33003−33−300−33−330000−2i2i2i−2i0000−i3−i3i3i3i3i3−i3−i30000000000i−i−ii000000
χ5322-2-2-22-2-122-22-1-1-12-2-21111-111-22-2-1-1-1-12211-211-11100-1-1−333−300−33−33003−33−300002i−2i−2i2i0000−i3−i3i3i3i3i3−i3−i30000000000−iii−i000000
χ5422-2-2-22-2-122-22-1-1-12-2-21111-111-22-2-1-1-1-12211-211-11100-1-1−333−300−33−33003−33−30000−2i2i2i−2i0000i3i3−i3−i3−i3−i3i3i30000000000i−i−ii000000
χ5522-2-2-2-2222-222-2-222-2-222-2-22-22-2-22-2-22-2-22-2-22222-2200-22000000000000000022-2-20000000000000000002200-2-2000000000000
χ5622-2-2-2-2222-222-2-222-2-222-2-22-22-2-22-2-22-2-22-2-22222-2200-220000000000000000-2-222000000000000000000-2-20022000000000000
χ5722-2-2-2-222-1-222-2-22-11122-2-2-1-2211-111-1-21-111-1-1-121-1001-10000−i3i3−i3−i3i3i3i3−i3i3i3−i3−i322-2-2000000000000000000-1-1−i3i311i3−i30000000000
χ5822-2-2-2-222-1-222-2-22-11122-2-2-1-2211-111-1-21-111-1-1-121-1001-10000−i3i3−i3−i3i3i3i3−i3i3i3−i3−i3-2-22200000000000000000011i3−i3-1-1−i3i30000000000
χ5922-2-2-2-222-1-222-2-22-11122-2-2-1-2211-111-1-21-111-1-1-121-1001-10000i3−i3i3i3−i3−i3−i3i3−i3−i3i3i322-2-2000000000000000000-1-1i3−i311−i3i30000000000
χ6022-2-2-2-222-1-222-2-22-11122-2-2-1-2211-111-1-21-111-1-1-121-1001-10000i3−i3i3i3−i3−i3−i3i3−i3−i3i3i3-2-22200000000000000000011−i3i3-1-1i3−i30000000000
χ614444444-2-2444-2-2-2-2-2-2-2-2-2-21-2-2-2-2-2111-2-2-211-211-2114411-2-2-2-2-2-21111-2-211110000000000000000000000000000000000000000
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χ864-44i−4i0004400000-4-44i−4i004i−4i40000000-40004i−4i0000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ874-44i−4i000-24000−2i32i32-44i−4i23−23−2i2i-200000−2i32i32000−2i2i023−2300000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ2300000000000000000000
χ884-44i−4i000-24000−2i32i32-44i−4i23−23−2i2i-200000−2i32i32000−2i2i023−230000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ2300000000000000000000
χ894-44i−4i000-240002i3−2i32-44i−4i−2323−2i2i-2000002i3−2i32000−2i2i0−232300000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ2300000000000000000000
χ904-44i−4i000-240002i3−2i32-44i−4i−2323−2i2i-2000002i3−2i32000−2i2i0−23230000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ2300000000000000000000
χ914-4−4i4i0004400000-4-4−4i4i00−4i4i40000000-4000−4i4i0000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ924-4−4i4i0004400000-4-4−4i4i00−4i4i40000000-4000−4i4i00000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ934-4−4i4i000-24000−2i32i32-4−4i4i−23232i−2i-200000−2i32i320002i−2i0−23230000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ2300000000000000000000
χ944-4−4i4i000-24000−2i32i32-4−4i4i−23232i−2i-200000−2i32i320002i−2i0−232300000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ2300000000000000000000
χ954-4−4i4i000-240002i3−2i32-4−4i4i23−232i−2i-2000002i3−2i320002i−2i023−230000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ2300000000000000000000
χ964-4−4i4i000-240002i3−2i32-4−4i4i23−232i−2i-2000002i3−2i320002i−2i023−2300000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ2300000000000000000000
χ978-88i−8i0008-400000-84−4i4i008i−8i-400000004000−4i4i000000000000000000000000000000000000000000000000000000000000000000
χ988-88i−8i000-4-4000−4i34i344−4i4i43−43−4i4i2000002i3−2i3-20002i−2i0−2323000000000000000000000000000000000000000000000000000000000000000
χ998-88i−8i000-4-40004i3−4i344−4i4i−4343−4i4i200000−2i32i3-20002i−2i023−23000000000000000000000000000000000000000000000000000000000000000
χ1008-8−8i8i0008-400000-844i−4i00−8i8i-4000000040004i−4i000000000000000000000000000000000000000000000000000000000000000000
χ1018-8−8i8i000-4-4000−4i34i3444i−4i−43434i−4i2000002i3−2i3-2000−2i2i023−23000000000000000000000000000000000000000000000000000000000000000
χ1028-8−8i8i000-4-40004i3−4i3444i−4i43−434i−4i200000−2i32i3-2000−2i2i0−2323000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.