Finite Group Databasebeta

← Group #11784824

Character table — Group #11784824

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11112222222222222222224444444444444444444444888888888888888888881212121212121212121212122424242424242424242424242424242424243636363636363636
order1222222222336666666666223446666666666666666666666666666612121212121212124444121212121212121244444412121212121212121212121222224444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-11-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ61111111111111111111111-1-11-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111
χ71111111111111111111111-1-11-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-111
χ81111111111111111111111-1-11-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1111111-1-111-1-1
χ91-1-11111-1-1-11111-1-1-111-1-1-11-111-111111-1-1-111-1-1-1-11-1-111-1-111-1-111-1-111-1-111-1-1ii−i−iiiii−i−i−i−ii−ii−ii−iii−i−iii−i−iii−i−i1-11-11-11-1
χ101-1-11111-1-1-11111-1-1-111-1-1-11-111-111111-1-1-111-1-1-1-11-1-111-1-111-1-111-1-111-1-111-1-1ii−i−iiiii−i−i−i−ii−i−ii−iiii−i−i−i−iii−i−iii-11-11-11-11
χ111-1-11111-1-1-11111-1-1-111-1-1-11-111-111111-1-1-111-1-1-1-11-1-111-1-111-1-111-1-111-1-111-1-1−i−iii−i−i−i−iiiii−iii−ii−i−i−iiiii−i−iii−i−i-11-11-11-11
χ121-1-11111-1-1-11111-1-1-111-1-1-11-111-111111-1-1-111-1-1-1-11-1-111-1-111-1-111-1-111-1-111-1-1−i−iii−i−i−i−iiiii−ii−ii−ii−i−iii−i−iii−i−iii1-11-11-11-1
χ131-1-11111-1-1-11111-1-1-111-1-1-1-111-1111111-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-111ii−i−iiiii−i−i−i−i−iii−i−ii−i−iiiii−i−i−i−iii1-1-111-1-11
χ141-1-11111-1-1-11111-1-1-111-1-1-1-111-1111111-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-111ii−i−iiiii−i−i−i−i−ii−iii−i−i−iii−i−iiiii−i−i-111-1-111-1
χ151-1-11111-1-1-11111-1-1-111-1-1-1-111-1111111-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-111−i−iii−i−i−i−iiiiii−ii−i−iiii−i−iii−i−i−i−iii-111-1-111-1
χ161-1-11111-1-1-11111-1-1-111-1-1-1-111-1111111-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-111−i−iii−i−i−i−iiiiii−i−iii−iii−i−i−i−iiiii−i−i1-1-111-1-11
χ1722222222222-1222-1-12-122222-12222-1-1-122-1-1-1-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1-1-12-12-1-1-1-1-10000000000000022220000-1-1-1-1-1-1-1-100000000
χ1822222222222-1222-1-12-122222-12222-1-1-122-1-1-1-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1-1-12-12-1-1-1-1-100000000000000-2-2-2-200001111111100000000
χ1922222222222-1222-1-12-1222-2-2-1-2-222-1-1-122-1-1-1-1-1-1-1-1-1-1-21-21-1-1-1-11111-21-2111110000000000000022-2-20000-1-1-1-1111100000000
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χ232222222222-12-1-1-122-12-1-1-1-2-2-1-2-2-1-1222-1-12-1-1-1-1-1-1-1221-21-2-1-1-1-111111-21-211112222-1-1-1-1-1-1-1-1-2-2000011110000000000000000
χ242222222222-12-1-1-122-12-1-1-1-2-2-1-2-2-1-1222-1-12-1-1-1-1-1-1-1221-21-2-1-1-1-111111-21-21111-2-2-2-211111111220000-1-1-1-10000000000000000
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χ2822222-2-22-2-22-1222-1-12-122222-1-2-2-2-2-111-2-2-1-1-1-1-1-1-1-1112-12-11111-1-1-1-1-21-2111110000000000000000000000−33−33−33−3300000000
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χ3022222-2-22-2-22-1222-1-12-1222-2-2-122-2-2-111-2-2-1-1-1-1-1-1-1-111-21-21111111112-12-1-1-1-1-10000000000000000000000−33−333−33−300000000
χ3122222-2-22-2-2-12-1-1-122-12-1-1-122-1-2-2112-2-2112-1-1-1-1-1-1-1-2-2-12-121111-1-1-1-11-21-211110000−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i30000000000000000
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χ392-2-22222-2-2-22-122-2112-1-2-2-22-2-12-222-1-1-1-2-21-1-11111-1112-1-21-1-111-1-1112-1-21-1-111000000000000002i−2i2i−2i0000−i−iii−i−iii00000000
χ402-2-22222-2-2-22-122-2112-1-2-2-22-2-12-222-1-1-1-2-21-1-11111-1112-1-21-1-111-1-1112-1-21-1-11100000000000000−2i2i−2i2i0000ii−i−iii−i−i00000000
χ412-2-22222-2-2-22-122-2112-1-2-2-2-22-1-2222-1-1-1-2-21-1-11111-111-212-1-1-11111-1-1-212-111-1-1000000000000002i−2i−2i2i0000−i−iiiii−i−i00000000
χ422-2-22222-2-2-22-122-2112-1-2-2-2-22-1-2222-1-1-1-2-21-1-11111-111-212-1-1-11111-1-1-212-111-1-100000000000000−2i2i2i−2i0000ii−i−i−i−iii00000000
χ432-2-22222-2-2-2-12-1-11-2-2-121112-2-12-2-1-122211-2-1-11111-1-2-2-121-2-1-111-1-111-121-2-1-1112i2i−2i−2i−i−i−i−iiiii2i−2i0000−i−iii0000000000000000
χ442-2-22222-2-2-2-12-1-11-2-2-121112-2-12-2-1-122211-2-1-11111-1-2-2-121-2-1-111-1-111-121-2-1-111−2i−2i2i2iiiii−i−i−i−i−2i2i0000ii−i−i0000000000000000
χ452-2-22222-2-2-2-12-1-11-2-2-12111-22-1-22-1-122211-2-1-11111-1-2-21-2-12-1-11111-1-11-2-1211-1-12i2i−2i−2i−i−i−i−iiiii−2i2i0000ii−i−i0000000000000000
χ462-2-22222-2-2-2-12-1-11-2-2-12111-22-1-22-1-122211-2-1-11111-1-2-21-2-12-1-11111-1-11-2-1211-1-1−2i−2i2i2iiiii−i−i−i−i2i−2i0000−i−iii0000000000000000
χ472-2-222-2-2-2222222-2-2-222-2-2-22-22-22-2-22-2-222-222-2-2-2-222222-2-2-2-22222-2-2-2-222-2-22200000000000000000000000000000000000000
χ482-2-222-2-2-2222222-2-2-222-2-2-2-2222-2-2-22-2-222-222-2-2-2-2222-2-222-2-222-2-22222-2-222-2-200000000000000000000000000000000000000
χ492-2-222-2-2-2222-122-2112-1-2-2-22-2-1-22-2-2-111221-1-11111-1-1-12-1-2111-1-1-1-111-212-111-1-10000000000000000000000−i3i3i3−i3−i3i3i3−i300000000
χ502-2-222-2-2-2222-122-2112-1-2-2-22-2-1-22-2-2-111221-1-11111-1-1-12-1-2111-1-1-1-111-212-111-1-10000000000000000000000i3−i3−i3i3i3−i3−i3i300000000
χ512-2-222-2-2-2222-122-2112-1-2-2-2-22-12-2-2-2-111221-1-11111-1-1-1-212-111-1-111-1-12-1-21-1-1110000000000000000000000−i3i3i3−i3i3−i3−i3i300000000
χ522-2-222-2-2-2222-122-2112-1-2-2-2-22-12-2-2-2-111221-1-11111-1-1-1-212-111-1-111-1-12-1-21-1-1110000000000000000000000i3−i3−i3i3−i3i3i3−i300000000
χ532-2-222-2-2-222-12-1-11-2-2-121112-2-1-22112-2-2-1-1-2-1-11111-122-121-211-1-1-1-1111-2-1211-1-1000033−3−3−3−3330000003−3−330000000000000000
χ542-2-222-2-2-222-12-1-11-2-2-121112-2-1-22112-2-2-1-1-2-1-11111-122-121-211-1-1-1-1111-2-1211-1-10000−3−33333−3−3000000−333−30000000000000000
χ552-2-222-2-2-222-12-1-11-2-2-12111-22-12-2112-2-2-1-1-2-1-11111-1221-2-1211-1-111-1-1-121-2-1-111000033−3−3−3−333000000−333−30000000000000000
χ562-2-222-2-2-222-12-1-11-2-2-12111-22-12-2112-2-2-1-1-2-1-11111-1221-2-1211-1-111-1-1-121-2-1-1110000−3−33333−3−30000003−3−330000000000000000
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χ954-4-44-4-4444-4-2-222222-2-2-2-22001002-222-2-22-2-1-1-1-1111-220000-111-13-3-330000-333-300000000000000000000000000000000000000
χ964-4-44-4-4444-4-2-222222-2-2-2-22001002-222-2-22-2-1-1-1-1111-220000-111-1-333-300003-3-3300000000000000000000000000000000000000
χ9788-8-80000008-4008-44-8400-800-4000000000000-44004000000000000000000000000000000000000000000000000000000000000
χ9888-8-8000000-4-4−4i34i3-4-4444−4i34i3400200000000002i3−2i32-22i3−2i3-2000000000000000000000000000000000000000000000000000000000000
χ9988-8-8000000-4-44i3−4i3-4-44444i3−4i340020000000000−2i32i32-2−2i32i3-2000000000000000000000000000000000000000000000000000000000000
χ1008-88-80000008-400-84-4-8400800-40000000000004-4004000000000000000000000000000000000000000000000000000000000000
χ1018-88-8000000-4-4−4i34i344-4444i3−4i3-400200000000002i3−2i3-22−2i32i3-2000000000000000000000000000000000000000000000000000000000000
χ1028-88-8000000-4-44i3−4i344-444−4i34i3-40020000000000−2i32i3-222i3−2i3-2000000000000000000000000000000000000000000000000000000000000

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