Finite Group Databasebeta

← Group #11786656

Character table — Group #11786656

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222222222444444444444444444888888888888888888888812121212121212121212121212121212121212122424242424242424242424242424363636367272
order124422233444666612121212121236666666612121212121212121266881212242424242424242424242424242424242244888888882424242424242424668812122424242424242424888888
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
χ5111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1
χ6111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111
χ7111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111
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
χ911-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-111-1-1-1111-111-11-11-111-1-1111111-1-1-1-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−i111-1-1-1ii−i−i11-1-1ii−i−ii−i
χ1011-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-111-1-1-1111-111-11-11-111-1-1111111-1-1-1-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii111-1-1-1−i−iii11-1-1−i−iii−ii
χ1111-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-111-1-1-1111-111-11-11-111-1-1111111-1-1-1-1-1-1-1-111ii−i−iii−i−iiiii−i−i−i−i-1-1-1111ii−i−i-1-111−i−iii−ii
χ1211-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-111-1-1-1111-111-11-11-111-1-1111111-1-1-1-1-1-1-1-111−i−iii−i−iii−i−i−i−iiiii-1-1-1111−i−iii-1-111ii−i−ii−i
χ1311-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-111-1-1-1111-111-1-111-1-1-111-1-1-1-1-1-111111111-1-1ii−i−i−i−iii−i−i−i−iiiii11-11-1-1ii−i−i-1-111ii−i−i−ii
χ1411-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-111-1-1-1111-111-1-111-1-1-111-1-1-1-1-1-111111111-1-1−i−iiiii−i−iiiii−i−i−i−i11-11-1-1−i−iii-1-111−i−iiii−i
χ1511-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-111-1-1-1111-111-1-111-1-1-111-1-1-1-1-1-1111111-1-111ii−i−i−i−iii−i−i−i−iiiii-1-11-111ii−i−i11-1-1−i−iiii−i
χ1611-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-111-1-1-1111-111-1-111-1-1-111-1-1-1-1-1-1111111-1-111−i−iiiii−i−iiiii−i−i−i−i-1-11-111−i−iii11-1-1ii−i−i−ii
χ1722222222-1222222-1-1-12222-122-1-1-1-1-1-12-1-1-1-1-1-12-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-122220000000000000000-1-122-1-10000-1-1-1-1000000
χ1822222222-1222222-1-1-12222-122-1-1-1-1-1-12-1-1-1-1-1-12-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000000000000011-2-21100001111000000
χ1922222222-1222222-1-1-12222-122-1-1-1-1-1-12-1-1-1-1-1-12-1-1-1-2-2-1-1-2-2-2-211111111111122220000000000000000-1-1-2-2-1-100001111000000
χ2022222222-1222222-1-1-12222-122-1-1-1-1-1-12-1-1-1-1-1-12-1-1-1-2-2-1-1-2-2-2-2111111111111-2-2-2-200000000000000001122110000-1-1-1-1000000
χ212222222-12222-1-1-1222-1-1-1-1-1-1-1222-1-1-1-12-1-12-1-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1000022222222-1-1-1-1-1-1-1-1000000-1-1-1-10000000000
χ222222222-12222-1-1-1222-1-1-1-1-1-1-1222-1-1-1-12-1-12-1-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-10000-2-2-2-2-2-2-2-21111111100000011110000000000
χ232222222-12222-1-1-1222-1-1-1-1-1-1-1222-1-1-1-12-1-12-1-1-12-1-1-2-2-1-11111-2-21111-2-2111100002222-2-2-2-211111111000000-1-1-1-10000000000
χ242222222-12222-1-1-1222-1-1-1-1-1-1-1222-1-1-1-12-1-12-1-1-12-1-1-2-2-1-11111-2-21111-2-211110000-2-2-2-22222-1-1-1-1-1-1-1-100000011110000000000
χ2522222-2-222-2-22-2-22222-2-22222-22-2-2-2-22-2222-2-2-22-22-200-2200000000000000002-22-200000000000000002-2002-200000000000000
χ2622222-2-222-2-22-2-22222-2-22222-22-2-2-2-22-2222-2-2-22-22-200-220000000000000000-22-220000000000000000-2200-2200000000000000
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χ2822222-2-22-1-2-22-2-22-1-1-1-2-222-12-2-11111-1-2-1-1-111121-11001-100003−333−3−33−333−3−3-22-2200000000000000001-1001-10000−33−33000000
χ2922222-2-22-1-2-22-2-22-1-1-1-2-222-12-2-11111-1-2-1-1-111121-11001-10000−33−3−333−33−3−3332-22-20000000000000000-1100-110000−33−33000000
χ3022222-2-22-1-2-22-2-22-1-1-1-2-222-12-2-11111-1-2-1-1-111121-11001-10000−33−3−333−33−3−333-22-2200000000000000001-1001-100003−33−3000000
χ312222-22-2222-2-222222222222-2-2-22-2222-2-222222-2-2-2-200-2-2000000000000000000000000000000000000000000000000002-22-200
χ322222-22-2222-2-222222222222-2-2-22-2222-2-222222-2-2-2-200-2-200000000000000000000000000000000000000000000000000-22-2200
χ332222-2-2222-22-2-2-22222-2-2222-22-2-22-2-222-222-2-2-2-22-22002-2000000000000000000002-22-20000000000000000002-22-20000000000
χ342222-2-2222-22-2-2-22222-2-2222-22-2-22-2-222-222-2-2-2-22-22002-200000000000000000000-22-22000000000000000000-22-220000000000
χ352222-2-22-12-22-211-122211-1-1-11-1-2-2211-1-1-2-1-1-211121-100-113−33−3003−33−3003−33−300002-22-2000033−3−333−3−3000000-11-110000000000
χ362222-2-22-12-22-211-122211-1-1-11-1-2-2211-1-1-2-1-1-211121-100-113−33−3003−33−3003−33−30000-22-220000−3−333−3−3330000001-11-10000000000
χ372222-2-22-12-22-211-122211-1-1-11-1-2-2211-1-1-2-1-1-211121-100-11−33−3300−33−3300−33−3300002-22-20000−3−333−3−333000000-11-110000000000
χ382222-2-22-12-22-211-122211-1-1-11-1-2-2211-1-1-2-1-1-211121-100-11−33−3300−33−3300−33−330000-22-22000033−3−333−3−30000001-11-10000000000
χ3922-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22200-2-200000000000000002-2-2200000000000000002-200-2200000000000000
χ4022-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22200-2-20000000000000000-222-20000000000000000-22002-200000000000000
χ4122-2-22222-1-2-2-2222-111-2-2-2-2-122-1-1-1-1-1-1-2111111-21-1-1001100003−333−3−3−33−3−3332-2-220000000000000000-11001-100003−3−33000000
χ4222-2-22222-1-2-2-2222-111-2-2-2-2-122-1-1-1-1-1-1-2111111-21-1-1001100003−333−3−3−33−3−333-222-200000000000000001-100-110000−333−3000000
χ4322-2-22222-1-2-2-2222-111-2-2-2-2-122-1-1-1-1-1-1-2111111-21-1-100110000−33−3−3333−333−3−32-2-220000000000000000-11001-10000−333−3000000
χ4422-2-22222-1-2-2-2222-111-2-2-2-2-122-1-1-1-1-1-1-2111111-21-1-100110000−33−3−3333−333−3−3-222-200000000000000001-100-1100003−3−33000000
χ4522-2-22-2-22-122-2-2-22-11122-2-2-12-2-11111-12111-1-1-1-2-1-112-2-1122-2-2-1-1-1-1-1-111111122-2-20000000000000000-1-12-2110000-1-111000000
χ4622-2-22-2-22-122-2-2-22-11122-2-2-12-2-11111-12111-1-1-1-2-1-112-2-1122-2-2-1-1-1-1-1-1111111-2-222000000000000000011-22-1-1000011-1-1000000
χ4722-2-22-2-22-122-2-2-22-11122-2-2-12-2-11111-12111-1-1-1-2-1-11-22-11-2-222111111-1-1-1-1-1-122-2-20000000000000000-1-1-2211000011-1-1000000
χ4822-2-22-2-22-122-2-2-22-11122-2-2-12-2-11111-12111-1-1-1-2-1-11-22-11-2-222111111-1-1-1-1-1-1-2-2220000000000000000112-2-1-10000-1-111000000
χ4922-2-22-2-2-1222-211-12-2-2-1-111-1-112-2-211-1-1-2112-1-112-112-2-11-1-11122-1-1-1-1-2-2111100002i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii000000−i−iii0000000000
χ5022-2-22-2-2-1222-211-12-2-2-1-111-1-112-2-211-1-1-2112-1-112-112-2-11-1-11122-1-1-1-1-2-211110000−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i000000ii−i−i0000000000
χ5122-2-22-2-2-1222-211-12-2-2-1-111-1-112-2-211-1-1-2112-1-112-11-22-1111-1-1-2-2111122-1-1-1-100002i2i−2i−2i−2i−2i2i2iiiii−i−i−i−i000000−i−iii0000000000
χ5222-2-22-2-2-1222-211-12-2-2-1-111-1-112-2-211-1-1-2112-1-112-11-22-1111-1-1-2-2111122-1-1-1-10000−2i−2i2i2i2i2i−2i−2i−i−i−i−iiiii000000ii−i−i0000000000
χ5322-2-2-22-222-2222222-2-2-2-2-2-22-2-2-22-222222-2-2-2-2-222-2-20022000000000000000000002i−2i−2i2i0000000000000000002i−2i−2i2i0000000000
χ5422-2-2-22-222-2222222-2-2-2-2-2-22-2-2-22-222222-2-2-2-2-222-2-2002200000000000000000000−2i2i2i−2i000000000000000000−2i2i2i−2i0000000000
χ5522-2-2-22-2-12-222-1-1-12-2-21111-111-22-2-1-1-1-1211-211-121100-1-13−3−33003−33−300−33−3300002i−2i−2i2i0000i3i3−i3−i3−i3−i3i3i3000000−iii−i0000000000
χ5622-2-2-22-2-12-222-1-1-12-2-21111-111-22-2-1-1-1-1211-211-121100-1-13−3−33003−33−300−33−330000−2i2i2i−2i0000−i3−i3i3i3i3i3−i3−i3000000i−i−ii0000000000
χ5722-2-2-22-2-12-222-1-1-12-2-21111-111-22-2-1-1-1-1211-211-121100-1-1−333−300−33−33003−33−300002i−2i−2i2i0000−i3−i3i3i3i3i3−i3−i3000000−iii−i0000000000
χ5822-2-2-22-2-12-222-1-1-12-2-21111-111-22-2-1-1-1-1211-211-121100-1-1−333−300−33−33003−33−30000−2i2i2i−2i0000i3i3−i3−i3−i3−i3i3i3000000i−i−ii0000000000
χ5922-2-2-2-22222-22-2-222-2-222-2-22-22-2-22-2-22-22-2-22222-2-2200-22000000000000000000000000000000000000000000000000002i−2i−2i2i00
χ6022-2-2-2-22222-22-2-222-2-222-2-22-22-2-22-2-22-22-2-22222-2-2200-2200000000000000000000000000000000000000000000000000−2i2i2i−2i00
χ614444444-2-2444-2-2-2-2-2-2-2-2-2-21-2-2-2-2-2111-2-211-211-2-2114411-2-2-2-2-2-21111-2-211110000000000000000000000000000000000000000
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χ914-4−4i4i0004400000-4-4−4i4i00−4i4i40000000-400−4i4i00000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ924-4−4i4i0004400000-4-4−4i4i00−4i4i40000000-400−4i4i000000000000000000000000000000000002ζ5+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-200000−2i32i32002i−2i0−232300000000000000000000000000000000−2ζ5−2ζ132ζ5+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-200000−2i32i32002i−2i0−2323000000000000000000000000000000002ζ5+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-2000002i3−2i32002i−2i023−2300000000000000000000000000000000−2ζ5−2ζ132ζ5+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-2000002i3−2i32002i−2i023−23000000000000000000000000000000002ζ5+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-40000000400−4i4i0000000000000000000000000000000000000000000000000000000000000000000
χ988-88i−8i000-4-4000−4i34i344−4i4i43−43−4i4i2000002i3−2i3-2002i−2i0−23230000000000000000000000000000000000000000000000000000000000000000
χ998-88i−8i000-4-40004i3−4i344−4i4i−4343−4i4i200000−2i32i3-2002i−2i023−230000000000000000000000000000000000000000000000000000000000000000
χ1008-8−8i8i0008-400000-844i−4i00−8i8i-400000004004i−4i0000000000000000000000000000000000000000000000000000000000000000000
χ1018-8−8i8i000-4-4000−4i34i3444i−4i−43434i−4i2000002i3−2i3-200−2i2i023−230000000000000000000000000000000000000000000000000000000000000000
χ1028-8−8i8i000-4-40004i3−4i3444i−4i43−434i−4i200000−2i32i3-200−2i2i0−23230000000000000000000000000000000000000000000000000000000000000000

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