Finite Group Databasebeta

← Group #11787976

Character table — Group #11787976

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11112222222222222222224444444444444444444444888888888888888888881212121212121212121212122424242424242424242424242424242424243636363636363636
order1222222222336666666666223446666666666666666666666666666612121212121212124444121212121212121244444412121212121212121212121244444444
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
χ51111111111111111111111-1-11-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-11-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-11-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-11-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-1
χ911-1-111-11-1-111-1-1-1-1-1-111111-111-111111-1-1-111-1-1-1-11-1-111-1-111-1-111-1-11-11-111-1-111-1-11111-1-1-1-11-1i−ii−i11-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011-1-111-11-1-111-1-1-1-1-1-111111-111-111111-1-1-111-1-1-1-11-1-111-1-111-1-111-1-11-11-111-1-111-1-11111-1-1-1-11-1−ii−ii11-1-1−i−iii−i−iii−i−iii−i−iii
χ1111-1-111-11-1-111-1-1-1-1-1-111111-111-111111-1-1-111-1-1-1-11-1-111-1-111-1-111-1-11-11-111-1-1-1-111-1-1-1-11111-11i−ii−i-1-111ii−i−iii−i−i−i−iii−i−iii
χ1211-1-111-11-1-111-1-1-1-1-1-111111-111-111111-1-1-111-1-1-1-11-1-111-1-111-1-111-1-11-11-111-1-1-1-111-1-1-1-11111-11−ii−ii-1-111−i−iii−i−iiiii−i−iii−i−i
χ1311-1-111-11-1-111-1-1-1-1-1-11111-111-1111111-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-111-11-11-1-11111-1-11111-1-1-1-1-11i−i−ii-1-111ii−i−i−i−iiiii−i−i−i−iii
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χ1511-1-111-11-1-111-1-1-1-1-1-11111-111-1111111-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-111-11-11-1-111-1-111-1-1-1-111111-1i−i−ii11-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611-1-111-11-1-111-1-1-1-1-1-11111-111-1111111-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-111-11-11-1-111-1-111-1-1-1-111111-1−iii−i11-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222-12222-1-1-122222-12222-1-1-122-1-1-1-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000000000000022220000-1-1-1-1-1-1-1-100000000
χ1822222222222-12222-1-1-122222-12222-1-1-122-1-1-1-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000000000-2-2-2-200001111111100000000
χ1922222222222-12222-1-1-1222-2-2-1-2-222-1-1-122-1-1-1-1-1-1-1-1-1-1-21-21-1-1-1-1111111-2-211110000000000000022-2-20000-1-1-1-1111100000000
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χ222222222222-12-1-1-1-1222-1-1-122-122-1-1222-1-12-1-1-1-1-1-1-122-12-12-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-211111111-2-2000011110000000000000000
χ232222222222-12-1-1-1-1222-1-1-1-2-2-1-2-2-1-1222-1-12-1-1-1-1-1-1-1221-21-2-1-1-1-11111-2-21111112222-1-1-1-1-1-1-1-1-2-2000011110000000000000000
χ242222222222-12-1-1-1-1222-1-1-1-2-2-1-2-2-1-1222-1-12-1-1-1-1-1-1-1221-21-2-1-1-1-11111-2-2111111-2-2-2-211111111220000-1-1-1-10000000000000000
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χ272222-22-2-2-222222-2-2222-2-2200200-22-22-2-22-2-2-222-2-22-220000-22-2200000000000000000000000000000000000000000000002-22-2
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χ322222-2-222-2-22-12222-1-1-122222-1-2-2-2-211-1-2-2-1-1-1-1-1-1-1-1112-12-11111-1-1-1-111-2-211110000000000000000000000−33−33−33−3300000000
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χ342222-2-222-2-22-12222-1-1-1222-2-2-122-2-211-1-2-2-1-1-1-1-1-1-1-111-21-2111111111-1-122-1-1-1-10000000000000000000000−33−333−33−300000000
χ352222-2-222-2-2-12-1-1-1-1222-1-1-122-1-2-211-2-22112-1-1-1-1-1-1-1-2-2-12-121111-1-1-1-1-2-21111110000−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i30000000000000000
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χ372222-2-222-2-2-12-1-1-1-1222-1-1-1-2-2-12211-2-22112-1-1-1-1-1-1-1-2-21-21-21111111122-1-1-1-1-1-10000−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i30000000000000000
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χ3922-2-222-22-2-22-1-2-2-2-211-12222-2-12-222-1-1-1-2-21-1-11111-1112-1-21-1-111-1-111-112-2-1-111000000000000002i−2i2i−2i0000−i−iii−i−iii00000000
χ4022-2-222-22-2-22-1-2-2-2-211-12222-2-12-222-1-1-1-2-21-1-11111-1112-1-21-1-111-1-111-112-2-1-11100000000000000−2i2i−2i2i0000ii−i−iii−i−i00000000
χ4122-2-222-22-2-22-1-2-2-2-211-1222-22-1-2222-1-1-1-2-21-1-11111-111-212-1-1-11111-1-11-1-2211-1-1000000000000002i−2i−2i2i0000−i−iiiii−i−i00000000
χ4222-2-222-22-2-22-1-2-2-2-211-1222-22-1-2222-1-1-1-2-21-1-11111-111-212-1-1-11111-1-11-1-2211-1-100000000000000−2i2i2i−2i0000ii−i−i−i−iii00000000
χ4322-2-222-22-2-2-121111-2-22-1-1-12-2-12-2-1-122211-2-1-11111-1-2-2-121-2-1-111-1-1112-2-11-1-11122-2-2-1-1-1-111112-20000-1-1110000000000000000
χ4422-2-222-22-2-2-121111-2-22-1-1-12-2-12-2-1-122211-2-1-11111-1-2-2-121-2-1-111-1-1112-2-11-1-111-2-2221111-1-1-1-1-22000011-1-10000000000000000
χ4522-2-222-22-2-2-121111-2-22-1-1-1-22-1-22-1-122211-2-1-11111-1-2-21-2-12-1-11111-1-1-221-111-1-122-2-2-1-1-1-11111-22000011-1-10000000000000000
χ4622-2-222-22-2-2-121111-2-22-1-1-1-22-1-22-1-122211-2-1-11111-1-2-21-2-12-1-11111-1-1-221-111-1-1-2-2221111-1-1-1-12-20000-1-1110000000000000000
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χ5022-2-2-222-22-222-2-222-2-22-2-2200200-22-22-22-22-2-2-2-22222-20000-222-20000000000000000000000000000000000000000000000−2i2i2i−2i
χ5122-2-2-2-2-222222-2-2-2-2-2-222222-22-22-2-2-2-2222-222-2-2-2-222222-2-2-2-22222-2-2-22-22-2-22200000000000000000000000000000000000000
χ5222-2-2-2-2-222222-2-2-2-2-2-22222-2222-2-2-2-2-2222-222-2-2-2-2222-2-222-2-222-2-2222-22-222-2-200000000000000000000000000000000000000
χ5322-2-2-2-2-22222-1-2-2-2-211-12222-2-1-22-2-211-1221-1-11111-1-1-12-1-2111-1-1-1-1111-1-2211-1-10000000000000000000000−i3i3i3−i3−i3i3i3−i300000000
χ5422-2-2-2-2-22222-1-2-2-2-211-12222-2-1-22-2-211-1221-1-11111-1-1-12-1-2111-1-1-1-1111-1-2211-1-10000000000000000000000i3−i3−i3i3i3−i3−i3i300000000
χ5522-2-2-2-2-22222-1-2-2-2-211-1222-22-12-2-2-211-1221-1-11111-1-1-1-212-111-1-111-1-1-112-2-1-1110000000000000000000000−i3i3i3−i3i3−i3−i3i300000000
χ5622-2-2-2-2-22222-1-2-2-2-211-1222-22-12-2-2-211-1221-1-11111-1-1-1-212-111-1-111-1-1-112-2-1-1110000000000000000000000i3−i3−i3i3−i3i3i3−i300000000
χ5722-2-2-2-2-2222-121111-2-22-1-1-12-2-1-2211-2-22-1-1-2-1-11111-122-121-211-1-1-1-111-221-111-1-10000−i3−i3i3i3i3i3−i3−i3000000−i3i3i3−i30000000000000000
χ5822-2-2-2-2-2222-121111-2-22-1-1-12-2-1-2211-2-22-1-1-2-1-11111-122-121-211-1-1-1-111-221-111-1-10000i3i3−i3−i3−i3−i3i3i3000000i3−i3−i3i30000000000000000
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χ934-4-44000000-242-2−2i32i3-44-42i3−2i3200-200000000002i3−2i32-2−2i32i3200000000000000000000002i−2i−2i2i2ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ944-4-44000000-242-2−2i32i3-44-42i3−2i3200-200000000002i3−2i32-2−2i32i320000000000000000000000−2i2i2i−2i−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ954-4-44000000-242-22i3−2i3-44-4−2i32i3200-20000000000−2i32i32-22i3−2i3200000000000000000000002i−2i−2i2i2ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ964-4-44000000-242-22i3−2i3-44-4−2i32i3200-20000000000−2i32i32-22i3−2i320000000000000000000000−2i2i2i−2i−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ978-88-80000008-48-800-44400-800-4000000000000-44004000000000000000000000000000000000000000000000000000000000000
χ988-88-8000000-4-4-44−4i34i3-444−4i34i3400200000000002i3−2i32-22i3−2i3-2000000000000000000000000000000000000000000000000000000000000
χ998-88-8000000-4-4-444i3−4i3-4444i3−4i340020000000000−2i32i32-2−2i32i3-2000000000000000000000000000000000000000000000000000000000000
χ1008-8-880000008-4-88004-4400-800-40000000000004-4004000000000000000000000000000000000000000000000000000000000000
χ1018-8-88000000-4-44-4−4i34i34-444i3−4i340020000000000−2i32i3-222i3−2i3-2000000000000000000000000000000000000000000000000000000000000
χ1028-8-88000000-4-44-44i3−4i34-44−4i34i3400200000000002i3−2i3-22−2i32i3-2000000000000000000000000000000000000000000000000000000000000

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