Finite Group Databasebeta

← Group #11783110

Character table — Group #11783110

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222244444444444444444444888888888888888888888888999999991818181818181818181818181818181818181818363636363636363636363636
order1222444422443366666688881212121212121212666612121212242424242424242424242424242424242222444422448888888888888888444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii-1-1-1-1
χ511111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii1111
χ811111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i1111
χ911111111-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1
χ1111111111-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-1-111
χ1211111111-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-1-111
χ1311111111-1-1-1-111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ1411111111-1-1-1-111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ1511111111-1-1-1-111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i11-1-1
χ1611111111-1-1-1-111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii11-1-1
χ171111-1-1-1-111-1-111111111i−ii−i-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i1-11-11-11-1i−ii−i
χ181111-1-1-1-111-1-111111111i−ii−i-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii-11-11-11-11i−ii−i
χ191111-1-1-1-111-1-111111111i−ii−i-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-11111-1-111-1-1-1-111-1-111−ii−iii−ii−i−ii−ii
χ201111-1-1-1-111-1-111111111i−ii−i-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-111-1-111-1-11111-1-111-1-1i−ii−i−ii−ii−ii−ii
χ211111-1-1-1-111-1-111111111−ii−ii-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i-11-11-11-11−ii−ii
χ221111-1-1-1-111-1-111111111−ii−ii-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii1-11-11-11-1−ii−ii
χ231111-1-1-1-111-1-111111111−ii−ii-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-11111-1-111-1-1-1-111-1-111i−ii−i−ii−iii−ii−i
χ241111-1-1-1-111-1-111111111−ii−ii-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-111-1-111-1-11111-1-111-1-1−ii−iii−ii−ii−ii−i
χ251111-1-1-1-1-1-11111111111i−i−ii-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii1-1-111-1-11i−i−ii
χ261111-1-1-1-1-1-11111111111i−i−ii-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i-111-1-111-1i−i−ii
χ271111-1-1-1-1-1-11111111111i−i−ii-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-111-1-1-1-111-1-11111-1-1−iii−ii−i−ii−iii−i
χ281111-1-1-1-1-1-11111111111i−i−ii-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-111i−i−ii−iii−i−iii−i
χ291111-1-1-1-1-1-11111111111−iii−i-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii-111-1-111-1−iii−i
χ301111-1-1-1-1-1-11111111111−iii−i-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i1-1-111-1-11−iii−i
χ311111-1-1-1-1-1-11111111111−iii−i-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-111-1-1-1-111-1-11111-1-1i−i−ii−iii−ii−i−ii
χ321111-1-1-1-1-1-11111111111−iii−i-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-111−iii−ii−i−iii−i−ii
χ3322-2-22i−2i2i−2i00002222-2-2-2-200002i2i−2i−2i2i2i−2i−2i0000000000000000000000002-22-22i−2i2i−2i000000002ζ−2ζ2ζ3−2ζ300002ζ−2ζ2ζ3−2ζ3000000000000
χ3422-2-22i−2i2i−2i00002222-2-2-2-200002i2i−2i−2i2i2i−2i−2i0000000000000000000000002-22-22i−2i2i−2i00000000−2ζ2ζ−2ζ32ζ30000−2ζ2ζ−2ζ32ζ3000000000000
χ3522-2-22i−2i2i−2i00002222-2-2-2-200002i2i−2i−2i2i2i−2i−2i000000000000000000000000-22-22−2i2i−2i2i000000002ζ3−2ζ3−2ζ2ζ0000−2ζ32ζ32ζ−2ζ000000000000
χ3622-2-22i−2i2i−2i00002222-2-2-2-200002i2i−2i−2i2i2i−2i−2i000000000000000000000000-22-22−2i2i−2i2i00000000−2ζ32ζ32ζ−2ζ00002ζ3−2ζ3−2ζ2ζ000000000000
χ3722-2-2−2i2i−2i2i00002222-2-2-2-20000−2i−2i2i2i−2i−2i2i2i0000000000000000000000002-22-2−2i2i−2i2i000000002ζ3−2ζ32ζ−2ζ00002ζ3−2ζ32ζ−2ζ000000000000
χ3822-2-2−2i2i−2i2i00002222-2-2-2-20000−2i−2i2i2i−2i−2i2i2i0000000000000000000000002-22-2−2i2i−2i2i00000000−2ζ32ζ3−2ζ2ζ0000−2ζ32ζ3−2ζ2ζ000000000000
χ3922-2-2−2i2i−2i2i00002222-2-2-2-20000−2i−2i2i2i−2i−2i2i2i000000000000000000000000-22-222i−2i2i−2i000000002ζ−2ζ−2ζ32ζ30000−2ζ2ζ2ζ3−2ζ3000000000000
χ4022-2-2−2i2i−2i2i00002222-2-2-2-20000−2i−2i2i2i−2i−2i2i2i000000000000000000000000-22-222i−2i2i−2i00000000−2ζ2ζ2ζ3−2ζ300002ζ−2ζ−2ζ32ζ3000000000000
χ412-22-22i−2i−2i2i000022-2-222-2-200002i2i−2i−2i−2i−2i2i2i0000000000000000000000002-2-222i−2i−2i2i00002ζ3−2ζ32ζ−2ζ00002ζ3−2ζ32ζ−2ζ0000000000000000
χ422-22-22i−2i−2i2i000022-2-222-2-200002i2i−2i−2i−2i−2i2i2i0000000000000000000000002-2-222i−2i−2i2i0000−2ζ32ζ3−2ζ2ζ0000−2ζ32ζ3−2ζ2ζ0000000000000000
χ432-22-22i−2i−2i2i000022-2-222-2-200002i2i−2i−2i−2i−2i2i2i000000000000000000000000-222-2−2i2i2i−2i00002ζ−2ζ−2ζ32ζ30000−2ζ2ζ2ζ3−2ζ30000000000000000
χ442-22-22i−2i−2i2i000022-2-222-2-200002i2i−2i−2i−2i−2i2i2i000000000000000000000000-222-2−2i2i2i−2i0000−2ζ2ζ2ζ3−2ζ300002ζ−2ζ−2ζ32ζ30000000000000000
χ452-22-2−2i2i2i−2i000022-2-222-2-20000−2i−2i2i2i2i2i−2i−2i0000000000000000000000002-2-22−2i2i2i−2i00002ζ−2ζ2ζ3−2ζ300002ζ−2ζ2ζ3−2ζ30000000000000000
χ462-22-2−2i2i2i−2i000022-2-222-2-20000−2i−2i2i2i2i2i−2i−2i0000000000000000000000002-2-22−2i2i2i−2i0000−2ζ2ζ−2ζ32ζ30000−2ζ2ζ−2ζ32ζ30000000000000000
χ472-22-2−2i2i2i−2i000022-2-222-2-20000−2i−2i2i2i2i2i−2i−2i000000000000000000000000-222-22i−2i−2i2i00002ζ3−2ζ3−2ζ2ζ0000−2ζ32ζ32ζ−2ζ0000000000000000
χ482-22-2−2i2i2i−2i000022-2-222-2-20000−2i−2i2i2i2i2i−2i−2i000000000000000000000000-222-22i−2i−2i2i0000−2ζ32ζ32ζ−2ζ00002ζ3−2ζ3−2ζ2ζ0000000000000000
χ492-2-2222-2-22-22-222-2-2-2-22200002222-2-2-2-222-2-222-2-2000000000000000022-2-222-2-22-22-20000000000000000000000000000
χ502-2-2222-2-22-22-222-2-2-2-22200002222-2-2-2-222-2-222-2-20000000000000000-2-222-2-222-22-220000000000000000000000000000
χ512-2-2222-2-2-22-2222-2-2-2-22200002222-2-2-2-2-2-222-2-222000000000000000022-2-222-2-2-22-220000000000000000000000000000
χ522-2-2222-2-2-22-2222-2-2-2-22200002222-2-2-2-2-2-222-2-2220000000000000000-2-222-2-2222-22-20000000000000000000000000000
χ532-2-22-2-2222-2-2222-2-2-2-2220000-2-2-2-2222222-2-2-2-222000000000000000022-2-2-2-2222-2-220000000000000000000000000000
χ542-2-22-2-2222-2-2222-2-2-2-2220000-2-2-2-2222222-2-2-2-2220000000000000000-2-22222-2-2-222-20000000000000000000000000000
χ552-2-22-2-222-222-222-2-2-2-2220000-2-2-2-22222-2-22222-2-2000000000000000022-2-2-2-222-222-20000000000000000000000000000
χ562-2-22-2-222-222-222-2-2-2-2220000-2-2-2-22222-2-22222-2-20000000000000000-2-22222-2-22-2-220000000000000000000000000000
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χ664444-4-4-4-444-4-41-21-21-21-2−4i4i−4i4i-12-12-12-121-21-2-12-12−i−i2i2iii−2i−2i−i−i2i2iii−2i−2i0000000000000000000000000000000000000000
χ674444-4-4-4-444-4-4-21-21-21-214i−4i4i−4i2-12-12-12-1-21-212-12-1−2i−2iii2i2i−i−i−2i−2iii2i2i−i−i0000000000000000000000000000000000000000
χ684444-4-4-4-444-4-4-21-21-21-21−4i4i−4i4i2-12-12-12-1-21-212-12-12i2i−i−i−2i−2iii2i2i−i−i−2i−2iii0000000000000000000000000000000000000000
χ694444-4-4-4-4-4-4441-21-21-21-24i−4i−4i4i-12-12-12-12-12-121-21-2ii−2i−2i−i−i2i2i−i−i2i2iii−2i−2i0000000000000000000000000000000000000000
χ704444-4-4-4-4-4-4441-21-21-21-2−4i4i4i−4i-12-12-12-12-12-121-21-2−i−i2i2iii−2i−2iii−2i−2i−i−i2i2i0000000000000000000000000000000000000000
χ714444-4-4-4-4-4-444-21-21-21-214i−4i−4i4i2-12-12-12-12-12-1-21-21−2i−2iii2i2i−i−i2i2i−i−i−2i−2iii0000000000000000000000000000000000000000
χ724444-4-4-4-4-4-444-21-21-21-21−4i4i4i−4i2-12-12-12-12-12-1-21-212i2i−i−i−2i−2iii−2i−2iii2i2i−i−i0000000000000000000000000000000000000000
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χ744-4-4444-4-44-44-41-2-12-121-200001-21-2-12-121-2-121-2-12−3i3i00−3i3i00−3i3i00−3i3i000000000000000000000000000000000000000000
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χ764-4-4444-4-44-44-4-212-12-1-210000-21-212-12-1-212-1-212-100−3i3i00−3i3i00−3i3i00−3i3i0000000000000000000000000000000000000000
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χ814-4-44-4-4444-4-441-2-12-121-20000-12-121-21-21-2-12-121-23-300-33003-300-33000000000000000000000000000000000000000000
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χ8988-8-88i−8i8i−8i00002-42-4-24-2400002i−4i−2i4i2i−4i−2i4i0000000000000000000000000000000000000000000000000000000000000000
χ9088-8-88i−8i8i−8i0000-42-424-24-20000−4i2i4i−2i−4i2i4i−2i0000000000000000000000000000000000000000000000000000000000000000
χ9188-8-8−8i8i−8i8i00002-42-4-24-240000−2i4i2i−4i−2i4i2i−4i0000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8−8i8i−8i8i0000-42-424-24-200004i−2i−4i2i4i−2i−4i2i0000000000000000000000000000000000000000000000000000000000000000
χ938-88-88i−8i−8i8i00002-4-242-4-2400002i−4i−2i4i−2i4i2i−4i0000000000000000000000000000000000000000000000000000000000000000
χ948-88-88i−8i−8i8i0000-424-2-424-20000−4i2i4i−2i4i−2i−4i2i0000000000000000000000000000000000000000000000000000000000000000
χ958-88-8−8i8i8i−8i00002-4-242-4-240000−2i4i2i−4i2i−4i−2i4i0000000000000000000000000000000000000000000000000000000000000000
χ968-88-8−8i8i8i−8i0000-424-2-424-200004i−2i−4i2i−4i2i4i−2i0000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.