Finite Group Databasebeta

← Group #11793867

Character table — Group #11793867

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111222222222222222222444444444444444444888888888888888888888812121212121212121212121224242424242424242424242424242424242472727272
order1244222334446666121212121212366666666121212121212121212668812122424242424242424242424242424242444441212121212121212224466668812121212242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111-11-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-11-11-1-111-1-1-1-111-1-1-1-111-1-1
χ6111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ7111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111
χ8111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11111-1-1111111-1-1
χ922222222-1222222-122-1-122-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000020200-1-12200-1-1-1-1-1-10000
χ1022222222-1222222-122-1-122-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000-20-20011-2-2001111110000
χ1122222222-1222222-122-1-122-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-2-2-1-1-2-2-2-2111111111111000000000000020200-1-1-2-200-1-111110000
χ1222222222-1222222-122-1-122-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-2-2-1-1-2-2-2-21111111111110000000000000-20-20011220011-1-1-1-10000
χ132222222-12222-1-1-12-1-122-1-1-1-1222-1-1-1-1-1-12-1-12-1-12-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12020-1-10000-1-10000000000
χ142222222-12222-1-1-12-1-122-1-1-1-1222-1-1-1-1-1-12-1-12-1-12-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-20-20110000110000000000
χ152222222-12222-1-1-12-1-122-1-1-1-1222-1-1-1-1-1-12-1-12-1-12-1-1-2-2-1-11111-2-2-2-2111111112222-1-1-1-1-1-1-1-1-20-20110000110000000000
χ162222222-12222-1-1-12-1-122-1-1-1-1222-1-1-1-1-1-12-1-12-1-12-1-1-2-2-1-11111-2-2-2-211111111-2-2-2-2111111112020-1-10000-1-10000000000
χ1722222-2-2222-2-222222222222-22-2-2222-2-2-2-222222-2-2-200-2-200000000000000000000000000000000000000000000002i−2i00
χ1822222-2-2222-2-222222222222-22-2-2222-2-2-2-222222-2-2-200-2-20000000000000000000000000000000000000000000000−2i2i00
χ192222-22-222-22-2-2-2222222-2-222-22-2-2-22-22-2222-2-2-2-22-22i−2i2-22i2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000
χ202222-22-222-22-2-2-2222222-2-222-22-2-2-22-22-2222-2-2-2-22-2−2i2i2-2−2i−2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000
χ212222-22-22-1-22-2-2-22-122-1-1-2-2-121-1111-1-22-2-1-1-11111-112i−2i-112i2i−2i−2i−i−iii−i−i−i−iiiii000000000000000000−i3i30000−i3i333−3−30000
χ222222-22-22-1-22-2-2-22-122-1-1-2-2-121-1111-1-22-2-1-1-11111-112i−2i-112i2i−2i−2i−i−iii−i−i−i−iiiii000000000000000000i3−i30000i3−i3−3−3330000
χ232222-22-22-1-22-2-2-22-122-1-1-2-2-121-1111-1-22-2-1-1-11111-11−2i2i-11−2i−2i2i2iii−i−iiiii−i−i−i−i000000000000000000−i3i30000−i3i3−3−3330000
χ242222-22-22-1-22-2-2-22-122-1-1-2-2-121-1111-1-22-2-1-1-11111-11−2i2i-11−2i−2i2i2iii−i−iiiii−i−i−i−i000000000000000000i3−i30000i3−i333−3−30000
χ252222-22-2-12-22-211-12-1-12211-1-1-22-211-11-112-1-1-211-2-112i−2i-11−i−iii2i2i−2i−2i−i−i−i−iiiii00003333−3−3−3−30000−i3i30000−i3i30000000000
χ262222-22-2-12-22-211-12-1-12211-1-1-22-211-11-112-1-1-211-2-112i−2i-11−i−iii2i2i−2i−2i−i−i−i−iiiii0000−3−3−3−333330000i3−i30000i3−i30000000000
χ272222-22-2-12-22-211-12-1-12211-1-1-22-211-11-112-1-1-211-2-11−2i2i-11ii−i−i−2i−2i2i2iiiii−i−i−i−i00003333−3−3−3−30000i3−i30000i3−i30000000000
χ282222-22-2-12-22-211-12-1-12211-1-1-22-211-11-112-1-1-211-2-11−2i2i-11ii−i−i−2i−2i2i2iiiii−i−i−i−i0000−3−3−3−333330000−i3i30000−i3i30000000000
χ292222-2-2222-2-22-2-2222222-2-22-2-2-22-2-222-22-222-2-2-22-2200-220000000000000000000000000000000000000000000000002-2
χ302222-2-2222-2-22-2-2222222-2-22-2-2-22-2-222-22-222-2-2-22-2200-22000000000000000000000000000000000000000000000000-22
χ3122-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22200-2-20000000000000000000000000000000000002i−2i00002i−2i2i−2i0000
χ3222-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22200-2-2000000000000000000000000000000000000−2i2i0000−2i2i−2i2i0000
χ3322-2-22222-1-2-2-2222-1-2-211-2-2-12-1-1-1-1-1-12-2-21111111-1-1001100003−33−333−3−333−3−3000000000000000000−i3i32i−2i00i3−i3−ii−ii0000
χ3422-2-22222-1-2-2-2222-1-2-211-2-2-12-1-1-1-1-1-12-2-21111111-1-1001100003−33−333−3−333−3−3000000000000000000i3−i3−2i2i00−i3i3i−ii−i0000
χ3522-2-22222-1-2-2-2222-1-2-211-2-2-12-1-1-1-1-1-12-2-21111111-1-100110000−33−33−3−333−3−333000000000000000000−i3i3−2i2i00i3−i3i−ii−i0000
χ3622-2-22222-1-2-2-2222-1-2-211-2-2-12-1-1-1-1-1-12-2-21111111-1-100110000−33−33−3−333−3−333000000000000000000i3−i32i−2i00−i3i3−ii−ii0000
χ3722-2-22-2-222-2222222-2-2-2-2-2-22-22-2-2222-2222-2-2-2-2-22-2-20022000000000000000000000000000020-20220000-2-20000000000
χ3822-2-22-2-222-2222222-2-2-2-2-2-22-22-2-2222-2222-2-2-2-2-22-2-200220000000000000000000000000000-2020-2-20000220000000000
χ3922-2-22-2-2-12-222-1-1-1211-2-211-112-2-2-1-1-11-1-1211-21121100-1-13−33−300003−33−33−33−3000033−3−333−3−320-20-1-10000110000000000
χ4022-2-22-2-2-12-222-1-1-1211-2-211-112-2-2-1-1-11-1-1211-21121100-1-13−33−300003−33−33−33−30000−3−333−3−333-2020110000-1-10000000000
χ4122-2-22-2-2-12-222-1-1-1211-2-211-112-2-2-1-1-11-1-1211-21121100-1-1−33−330000−33−33−33−33000033−3−333−3−3-2020110000-1-10000000000
χ4222-2-22-2-2-12-222-1-1-1211-2-211-112-2-2-1-1-11-1-1211-21121100-1-1−33−330000−33−33−33−330000−3−333−3−33320-20-1-10000110000000000
χ4322-2-2-22-2222-22-2-222-2-2-2-22222-22-2-2-22-2-22-2-2-222222-200-220000000000000000000000000000020-200220000-2-200000000
χ4422-2-2-22-2222-22-2-222-2-2-2-22222-22-2-2-22-2-22-2-2-222222-200-2200000000000000000000000000000-20200-2-200002200000000
χ4522-2-2-22-22-12-22-2-22-1-2-21122-121-1111-1-2-22111-1-1-1-1-11001-10000−i3i3i3−i3−i3−i3i3i3i3i3−i3−i3000000000000020-200-1-1000011−i3i3i3−i30000
χ4622-2-2-22-22-12-22-2-22-1-2-21122-121-1111-1-2-22111-1-1-1-1-11001-10000−i3i3i3−i3−i3−i3i3i3i3i3−i3−i30000000000000-20200110000-1-1i3−i3−i3i30000
χ4722-2-2-22-22-12-22-2-22-1-2-21122-121-1111-1-2-22111-1-1-1-1-11001-10000i3−i3−i3i3i3i3−i3−i3−i3−i3i3i3000000000000020-200-1-1000011i3−i3−i3i30000
χ4822-2-2-22-22-12-22-2-22-1-2-21122-121-1111-1-2-22111-1-1-1-1-11001-10000i3−i3−i3i3i3i3−i3−i3−i3−i3i3i30000000000000-20200110000-1-1−i3i3i3−i30000
χ4922-2-2-2-222222-2-2-222-2-2-2-2222-2-2-22-2-2222-22-2-2222-2-22002-2000000000000000022-2-222-2-2-2-2220000000000000000000000
χ5022-2-2-2-222222-2-2-222-2-2-2-2222-2-2-22-2-2222-22-2-2222-2-22002-20000000000000000-2-222-2-22222-2-20000000000000000000000
χ5122-2-2-2-22-1222-211-1211-2-2-1-1-11-2-2211-1-1-112112-1-1-21-100-11−i3i3i3−i30000−i3i3−i3i3i3−i3i3−i322-2-2-1-11111-1-10000−i3i30000i3−i30000000000
χ5222-2-2-2-22-1222-211-1211-2-2-1-1-11-2-2211-1-1-112112-1-1-21-100-11−i3i3i3−i30000−i3i3−i3i3i3−i3i3−i3-2-22211-1-1-1-1110000i3−i30000−i3i30000000000
χ5322-2-2-2-22-1222-211-1211-2-2-1-1-11-2-2211-1-1-112112-1-1-21-100-11i3−i3−i3i30000i3−i3i3−i3−i3i3−i3i322-2-2-1-11111-1-10000i3−i30000−i3i30000000000
χ5422-2-2-2-22-1222-211-1211-2-2-1-1-11-2-2211-1-1-112112-1-1-21-100-11i3−i3−i3i30000i3−i3i3−i3−i3i3−i3i3-2-22211-1-1-1-1110000−i3i30000i3−i30000000000
χ554444444-2-2444-2-2-2-2-2-2-2-2-2-21-2-2-2-2111-2-2-2-211-211-2114411-2-2-2-2-2-2-2-2111111110000000000000000000000000000000000
χ564444444-2-2444-2-2-2-2-2-2-2-2-2-21-2-2-2-2111-2-2-2-211-211-211-4-41122222222-1-1-1-1-1-1-1-10000000000000000000000000000000000
χ5744444-4-44-24-4-4444-244-2-244-2-4-222-2-2-2-4-4-42-2-2-2-2-2222002200000000000000000000000000000000000000000000000000
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χ6044444-4-4-2-24-4-4-2-2-2-2-2-2-2-2-2-212-222111222211-2112-1-100-1-100000000-333-3-333-30000000000000000000000000000000000
χ614444-44-4-2-2-44-422-2-2-2-2-2-2221-22-22-1-112-22-2112-1-121-14i−4i1-1−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i0000000000000000000000000000000000
χ624444-44-4-2-2-44-422-2-2-2-2-2-2221-22-22-1-112-22-2112-1-121-1−4i4i1-12i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii0000000000000000000000000000000000
χ634444-4-444-2-4-44-4-44-244-2-2-4-4-2-422-222-24-442-2-2222-22-2002-200000000000000000000000000000000000000000000000000
χ644444-4-44-24-4-4422-24-2-24422-22-4-4422-2-22-2-4-2-2-42242-2002-200000000000000000000000000000000000000000000000000
χ654444-4-44-2-2-4-4422-2-2-2-2-2-2221222-2-1-11-22-22112-1-1-2-1100-11000000003i−3i−3i3i−3i3i3i−3i0000000000000000000000000000000000
χ664444-4-44-2-2-4-4422-2-2-2-2-2-2221222-2-1-11-22-22112-1-1-2-1100-1100000000−3i3i3i−3i3i−3i−3i3i0000000000000000000000000000000000
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χ6944-4-4444-2-2-4-4-4-2-2-2-22222221-2-2-2-2111-2222-1-12-1-121100-1-10000−2323−232333−3−333−3−30000000000000000000000000000000000
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χ7244-4-44-4-4-2-2-444-2-2-2-222222212-2221112-2-2-2-1-12-1-1-2-1-10011−2323−232300003−33−33−33−30000000000000000000000000000000000
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χ7544-4-4-44-4-2-24-4422-2-22222-2-21-22-22-1-1122-22-1-1-211-21-100-1100002i3−2i3−2i32i3−i3−i3i3i3i3i3−i3−i30000000000000000000000000000000000
χ7644-4-4-4-444-244-4-4-44-2-4-42244-2-422-222-244-4-222-2-2-222-200-2200000000000000000000000000000000000000000000000000
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χ7844-4-4-4-44-2-244-422-2-22222-2-21222-2-1-11-2-22-2-1-1-2112-11001-12i3−2i3−2i32i30000−i3i3−i3i3i3−i3i3−i30000000000000000000000000000000000
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χ824-44i−4i000-24000−2i32i32-4−2i2i4i−4i23−23-20000−2i32i320000−2i2i023−2300000000000000000000000-22−2i2i1+3−1−3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ111−3−1+30000000000000000000000
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χ844-44i−4i000-240002i3−2i32-4−2i2i4i−4i−2323-200002i3−2i320000−2i2i0−232300000000000000000000000-22−2i2i1−3−1+3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ111+3−1−30000000000000000000000
χ854-4−4i4i0004400000-4-4−4i4i−4i4i004000000-40000−4i4i000000000000000000000000002-2−2i2i2-2−2i2i−2i2i2-20000000000000000000000
χ864-4−4i4i0004400000-4-4−4i4i−4i4i004000000-40000−4i4i00000000000000000000000000-222i−2i-222i−2i2i−2i-220000000000000000000000
χ874-4−4i4i000-24000−2i32i32-42i−2i−4i4i−2323-20000−2i32i3200002i−2i0−2323000000000000000000000002-2−2i2i−1+31−3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−1−31+30000000000000000000000
χ884-4−4i4i000-24000−2i32i32-42i−2i−4i4i−2323-20000−2i32i3200002i−2i0−232300000000000000000000000-222i−2i1−3−1+3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ111+3−1−30000000000000000000000
χ894-4−4i4i000-240002i3−2i32-42i−2i−4i4i23−23-200002i3−2i3200002i−2i023−23000000000000000000000002-2−2i2i−1−31+3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−1+31−30000000000000000000000
χ904-4−4i4i000-240002i3−2i32-42i−2i−4i4i23−23-200002i3−2i3200002i−2i023−2300000000000000000000000-222i−2i1+3−1−3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ111−3−1+30000000000000000000000
χ918-88i−8i0008-400000-848i−8i−4i4i00-400000040000−4i4i000000000000000000000000000000000000000000000000000000000000
χ928-88i−8i000-4-4000−4i34i344−4i4i−4i4i43−43200002i3−2i3-200002i−2i0−2323000000000000000000000000000000000000000000000000000000000
χ938-88i−8i000-4-40004i3−4i344−4i4i−4i4i−434320000−2i32i3-200002i−2i023−23000000000000000000000000000000000000000000000000000000000
χ948-8−8i8i0008-400000-84−8i8i4i−4i00-4000000400004i−4i000000000000000000000000000000000000000000000000000000000000
χ958-8−8i8i000-4-4000−4i34i3444i−4i4i−4i−4343200002i3−2i3-20000−2i2i023−23000000000000000000000000000000000000000000000000000000000
χ968-8−8i8i000-4-40004i3−4i3444i−4i4i−4i43−4320000−2i32i3-20000−2i2i0−2323000000000000000000000000000000000000000000000000000000000

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