Finite Group Databasebeta

← Group #11786657

Character table — Group #11786657

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222222222444444444444444444888888888888888888888812121212121212121212121212121212121212122424242424242424242424242424363636367272
order12442223344466661212121212123666666661212121212121212126688121224242424242424242424242424242424888888888888242424242424242488242424242424242424242424224488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1
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
χ5111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ6111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ7111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ8111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1
χ911-1-11-1-1111-11-1-11111-1-1-1-1111-1-1-1-1-1111-1-1-1111-11-11-11-111-1-1111111-1-1-1-1-1-1ii−i−iii−i−iii−i−iiiii−i−i−i−ii−iii−i−iii−i−iii−i−i11-1-11-1
χ1011-1-11-1-1111-11-1-11111-1-1-1-1111-1-1-1-1-1111-1-1-1111-11-11-11-111-1-1111111-1-1-1-1-1-1ii−i−i−i−iiiii−i−iiiii−i−i−i−i−iiii−i−i−i−iii−i−iii-1-111-11
χ1111-1-11-1-1111-11-1-11111-1-1-1-1111-1-1-1-1-1111-1-1-1111-11-11-11-111-1-1111111-1-1-1-1-1-1−i−iiiii−i−i−i−iii−i−i−i−iiiiii−i−i−iiiii−i−iii−i−i-1-111-11
χ1211-1-11-1-1111-11-1-11111-1-1-1-1111-1-1-1-1-1111-1-1-1111-11-11-11-111-1-1111111-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−i−i−iiiii−ii−i−iii−i−iii−i−iii11-1-11-1
χ1311-1-11-1-1111-11-1-11111-1-1-1-1111-1-1-1-1-1111-1-1-1111-11-1-111-1-1-111-1-1-1-1-1-1111111ii−i−iii−i−i−i−iii−i−i−i−iiiii−iiii−i−iii−i−i−i−iii11-1-1-11
χ1411-1-11-1-1111-11-1-11111-1-1-1-1111-1-1-1-1-1111-1-1-1111-11-1-111-1-1-111-1-1-1-1-1-1111111ii−i−i−i−iii−i−iii−i−i−i−iiiiii−iii−i−i−i−iiiii−i−i-1-1111-1
χ1511-1-11-1-1111-11-1-11111-1-1-1-1111-1-1-1-1-1111-1-1-1111-11-1-111-1-1-111-1-1-1-1-1-1111111−i−iiiii−i−iii−i−iiiii−i−i−i−i−ii−i−iiiii−i−i−i−iii-1-1111-1
χ1611-1-11-1-1111-11-1-11111-1-1-1-1111-1-1-1-1-1111-1-1-1111-11-1-111-1-1-111-1-1-1-1-1-1111111−i−iii−i−iiiii−i−iiiii−i−i−i−ii−i−i−iii−i−iiiii−i−i11-1-1-11
χ1722222222-1222222-12222-1-1-12-12-1-1-1-1-12-1-1-1-1-1-1-12-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-100002222000000000000220000-1-1-1-1-1-1-1-1000000
χ1822222222-1222222-12222-1-1-12-12-1-1-1-1-12-1-1-1-1-1-1-12-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-2000000000000-2-2000011111111000000
χ1922222222-1222222-12222-1-1-12-12-1-1-1-1-12-1-1-1-1-1-1-12-1-1-2-2-1-1-2-2-2-211111111111100002222000000000000-2-20000-1-1-1-11111000000
χ2022222222-1222222-12222-1-1-12-12-1-1-1-1-12-1-1-1-1-1-1-12-1-1-2-2-1-1-2-2-2-21111111111110000-2-2-2-20000000000002200001111-1-1-1-1000000
χ212222222-12222-1-1-12-1-1-1-122-1-12-122-1-1-1-122-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1222200002222-1-1-1-1-1-1-1-100-1-1-1-100000000000000
χ222222222-12222-1-1-12-1-1-1-122-1-12-122-1-1-1-122-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-20000-2-2-2-21111111100111100000000000000
χ232222222-12222-1-1-12-1-1-1-122-1-12-122-1-1-1-122-1-12-1-1-1-1-1-2-2-1-11111-2-21111-2-2111122220000-2-2-2-21111111100-1-1-1-100000000000000
χ242222222-12222-1-1-12-1-1-1-122-1-12-122-1-1-1-122-1-12-1-1-1-1-1-2-2-1-11111-2-21111-2-21111-2-2-2-200002222-1-1-1-1-1-1-1-100111100000000000000
χ2522222-2-222-22-2-2-222-2-22222222-2-2-2-2-22-2-2222-2-2-222-200-22000000000000000000000000000000000000000000000000002-22-200
χ2622222-2-222-22-2-2-222-2-22222222-2-2-2-2-22-2-2222-2-2-222-200-2200000000000000000000000000000000000000000000000000-22-2200
χ272222-22-2222-2-222222222222-2-2-22-2222-2-2-222222-2-2-200-2-2000000000000000000002-22-20000000000000000002-22-20000000000
χ282222-22-2222-2-222222222222-2-2-22-2222-2-2-222222-2-2-200-2-200000000000000000000-22-22000000000000000000-22-220000000000
χ292222-22-22-12-2-2222-12222-1-1-1-21-2-11-1-1-1-211-1-1-1-1-1-21100110000−i3i3−i3−i3i3i3−i3i3−i3−i3i3i300002-22-2000000000000000000-11-11−i3i3−i3i3000000
χ302222-22-22-12-2-2222-12222-1-1-1-21-2-11-1-1-1-211-1-1-1-1-1-21100110000−i3i3−i3−i3i3i3−i3i3−i3−i3i3i30000-22-220000000000000000001-11-1i3−i3i3−i3000000
χ312222-22-22-12-2-2222-12222-1-1-1-21-2-11-1-1-1-211-1-1-1-1-1-21100110000i3−i3i3i3−i3−i3i3−i3i3i3−i3−i300002-22-2000000000000000000-11-11i3−i3i3−i3000000
χ322222-22-22-12-2-2222-12222-1-1-1-21-2-11-1-1-1-211-1-1-1-1-1-21100110000i3−i3i3i3−i3−i3i3−i3i3i3−i3−i30000-22-220000000000000000001-11-1−i3i3−i3i3000000
χ332222-2-2222-2-22-2-222-2-222222-2-22-22-2-2222-222-2-2-2-2-22002-200000000000000002-22-20000000000000000002-22-200000000000000
χ342222-2-2222-2-22-2-222-2-222222-2-22-22-2-2222-222-2-2-2-2-22002-20000000000000000-22-22000000000000000000-22-2200000000000000
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χ362222-2-22-12-2-2211-1211-1-122-11-2-1-2211-1-12-2-1-1-21111-100-113−33−3003−33−3003−33−3-22-2200000000−3−333−3−333001-11-100000000000000
χ372222-2-22-12-2-2211-1211-1-122-11-2-1-2211-1-12-2-1-1-21111-100-11−33−3300−33−3300−33−332-22-200000000−3−333−3−33300-11-1100000000000000
χ382222-2-22-12-2-2211-1211-1-122-11-2-1-2211-1-12-2-1-1-21111-100-11−33−3300−33−3300−33−33-22-220000000033−3−333−3−3001-11-100000000000000
χ3922-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22200-2-2000000000000000000000000000000000000000000000000002-2-2200
χ4022-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22200-2-200000000000000000000000000000000000000000000000000-222-200
χ4122-2-22-2-22-12-22-2-22-122-2-211-12-1-21111-12-1111-1-1-1-2-112-2-1122-2-2-1-1-1-1-1-111111100002i2i−2i−2i0000000000002i−2i0000−i−iii−i−iii000000
χ4222-2-22-2-22-12-22-2-22-122-2-211-12-1-21111-12-1111-1-1-1-2-112-2-1122-2-2-1-1-1-1-1-11111110000−2i−2i2i2i000000000000−2i2i0000ii−i−iii−i−i000000
χ4322-2-22-2-22-12-22-2-22-122-2-211-12-1-21111-12-1111-1-1-1-2-11-22-11-2-222111111-1-1-1-1-1-100002i2i−2i−2i000000000000−2i2i0000−i−iiiii−i−i000000
χ4422-2-22-2-22-12-22-2-22-122-2-211-12-1-21111-12-1111-1-1-1-2-11-22-11-2-222111111-1-1-1-1-1-10000−2i−2i2i2i0000000000002i−2i0000ii−i−i−i−iii000000
χ4522-2-22-2-2-122-2211-12-1-111-2-2-1-121-2-211-1-12-2112-1-11-112-2-11-1-11122-1-1-1-1-2-211112i2i−2i−2i00002i2i−2i−2i−i−i−i−iiiii00−i−iii00000000000000
χ4622-2-22-2-2-122-2211-12-1-111-2-2-1-121-2-211-1-12-2112-1-11-112-2-11-1-11122-1-1-1-1-2-21111−2i−2i2i2i0000−2i−2i2i2iiiii−i−i−i−i00ii−i−i00000000000000
χ4722-2-22-2-2-122-2211-12-1-111-2-2-1-121-2-211-1-12-2112-1-11-11-22-1111-1-1-2-2111122-1-1-1-12i2i−2i−2i0000−2i−2i2i2iiiii−i−i−i−i00−i−iii00000000000000
χ4822-2-22-2-2-122-2211-12-1-111-2-2-1-121-2-211-1-12-2112-1-11-11-22-1111-1-1-2-2111122-1-1-1-1−2i−2i2i2i00002i2i−2i−2i−i−i−i−iiiii00ii−i−i00000000000000
χ4922-2-2-22-222-2222222-2-2-2-2-2-22-2-2-22-2222222-2-2-2-2-22-2-2002200000000000000002i−2i−2i2i0000000000000000002i−2i−2i2i00000000000000
χ5022-2-2-22-222-2222222-2-2-2-2-2-22-2-2-22-2222222-2-2-2-2-22-2-200220000000000000000−2i2i2i−2i000000000000000000−2i2i2i−2i00000000000000
χ5122-2-2-22-2-12-222-1-1-121111-2-2-11-212-2-1-1-1-12211-211-11100-1-13−3−33003−33−300−33−332i−2i−2i2i00000000i3i3−i3−i3−i3−i3i3i300−iii−i00000000000000
χ5222-2-2-22-2-12-222-1-1-121111-2-2-11-212-2-1-1-1-12211-211-11100-1-13−3−33003−33−300−33−33−2i2i2i−2i00000000−i3−i3i3i3i3i3−i3−i300i−i−ii00000000000000
χ5322-2-2-22-2-12-222-1-1-121111-2-2-11-212-2-1-1-1-12211-211-11100-1-1−333−300−33−33003−33−32i−2i−2i2i00000000−i3−i3i3i3i3i3−i3−i300−iii−i00000000000000
χ5422-2-2-22-2-12-222-1-1-121111-2-2-11-212-2-1-1-1-12211-211-11100-1-1−333−300−33−33003−33−3−2i2i2i−2i00000000i3i3−i3−i3−i3−i3i3i300i−i−ii00000000000000
χ5522-2-2-2-222222-2-2-22222-2-2-2-22-2-22-22-2-22-2-22-2-22222-2200-22000000000000000000002i−2i−2i2i0000000000000000002i−2i−2i2i0000000000
χ5622-2-2-2-222222-2-2-22222-2-2-2-22-2-22-22-2-22-2-22-2-22222-2200-2200000000000000000000−2i2i2i−2i000000000000000000−2i2i2i−2i0000000000
χ5722-2-2-2-222-122-2-2-22-122-2-211-1-2121-111-1-21-111-1-1-121-1001-10000−i3i3−i3−i3i3i3i3−i3i3i3−i3−i300002i−2i−2i2i000000000000000000−iii−i3−3−33000000
χ5822-2-2-2-222-122-2-2-22-122-2-211-1-2121-111-1-21-111-1-1-121-1001-10000−i3i3−i3−i3i3i3i3−i3i3i3−i3−i30000−2i2i2i−2i000000000000000000i−i−ii−333−3000000
χ5922-2-2-2-222-122-2-2-22-122-2-211-1-2121-111-1-21-111-1-1-121-1001-10000i3−i3i3i3−i3−i3−i3i3−i3−i3i3i300002i−2i−2i2i000000000000000000−iii−i−333−3000000
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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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χ854-44i−4i0004400000-4-4004i−4i4i−4i40000000-40004i−4i00000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
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χ874-44i−4i000-24000−2i32i32-423−23−2i2i4i−4i-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−4i000-24000−2i32i32-423−23−2i2i4i−4i-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−4i000-240002i3−2i32-4−2323−2i2i4i−4i-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−4i000-240002i3−2i32-4−2323−2i2i4i−4i-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
χ914-4−4i4i0004400000-4-400−4i4i−4i4i40000000-4000−4i4i0000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ924-4−4i4i0004400000-4-400−4i4i−4i4i40000000-4000−4i4i00000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ934-4−4i4i000-24000−2i32i32-4−23232i−2i−4i4i-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
χ944-4−4i4i000-24000−2i32i32-4−23232i−2i−4i4i-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
χ954-4−4i4i000-240002i3−2i32-423−232i−2i−4i4i-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
χ964-4−4i4i000-240002i3−2i32-423−232i−2i−4i4i-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−8i0008-400000-84008i−8i−4i4i-400000004000−4i4i000000000000000000000000000000000000000000000000000000000000000000
χ988-88i−8i000-4-4000−4i34i34443−43−4i4i−4i4i2000002i3−2i3-20002i−2i0−2323000000000000000000000000000000000000000000000000000000000000000
χ998-88i−8i000-4-40004i3−4i344−4343−4i4i−4i4i200000−2i32i3-20002i−2i023−23000000000000000000000000000000000000000000000000000000000000000
χ1008-8−8i8i0008-400000-8400−8i8i4i−4i-4000000040004i−4i000000000000000000000000000000000000000000000000000000000000000000
χ1018-8−8i8i000-4-4000−4i34i344−43434i−4i4i−4i2000002i3−2i3-2000−2i2i023−23000000000000000000000000000000000000000000000000000000000000000
χ1028-8−8i8i000-4-40004i3−4i34443−434i−4i4i−4i200000−2i32i3-2000−2i2i0−2323000000000000000000000000000000000000000000000000000000000000000

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