Finite Group Databasebeta

← Group #11786751

Character table — Group #11786751

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11112222222222222222224444444444444444444444888888888888888888881212121212121212121212122424242424242424242424242424242424243636363636363636
order122222334444666666666634444666666666121212121212121212121212121212121212121212121212121212124444121212121212121244888812121212242424242424242422444444
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
χ511111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-1
χ911-1-1-11111-11-1-1-1-111-1-111-11ii−i−i1-111-1-1-11-1111-1-1-11-1iiii−i−i−i−i11-1-1iiii−i−i−i−i11-1-11111-1-1-1-1i−i1-1i−iii−i−i11-1-1ii−i−i1-11-1i−ii−i
χ1011-1-1-11111-11-1-1-1-111-1-111-11ii−i−i1-111-1-1-11-1111-1-1-11-1iiii−i−i−i−i11-1-1iiii−i−i−i−i11-1-11111-1-1-1-1i−i-11−iiii−i−i-1-111−i−iii-11-11−ii−ii
χ1111-1-1-11111-11-1-1-1-111-1-111-11ii−i−i1-111-1-1-11-1111-1-1-11-1iiii−i−i−i−i11-1-1iiii−i−i−i−i-1-111-1-1-1-11111−ii1-1i−i−i−iii11-1-1ii−i−i-11-11−ii−ii
χ1211-1-1-11111-11-1-1-1-111-1-111-11ii−i−i1-111-1-1-11-1111-1-1-11-1iiii−i−i−i−i11-1-1iiii−i−i−i−i-1-111-1-1-1-11111−ii-11−ii−i−iii-1-111−i−iii1-11-1i−ii−i
χ1311-1-1-11111-11-1-1-1-111-1-111-11−i−iii1-111-1-1-11-1111-1-1-11-1−i−i−i−iiiii11-1-1−i−i−i−iiiii11-1-11111-1-1-1-1−ii1-1−ii−i−iii11-1-1−i−iii1-11-1−ii−ii
χ1411-1-1-11111-11-1-1-1-111-1-111-11−i−iii1-111-1-1-11-1111-1-1-11-1−i−i−i−iiiii11-1-1−i−i−i−iiiii11-1-11111-1-1-1-1−ii-11i−i−i−iii-1-111ii−i−i-11-11i−ii−i
χ1511-1-1-11111-11-1-1-1-111-1-111-11−i−iii1-111-1-1-11-1111-1-1-11-1−i−i−i−iiiii11-1-1−i−i−i−iiiii-1-111-1-1-1-11111i−i1-1−iiii−i−i11-1-1−i−iii-11-11i−ii−i
χ1611-1-1-11111-11-1-1-1-111-1-111-11−i−iii1-111-1-1-11-1111-1-1-11-1−i−i−i−iiiii11-1-1−i−i−i−iiiii-1-111-1-1-1-11111i−i-11i−iii−i−i-1-111ii−i−i1-11-1−ii−ii
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χ1822222222-2-2-2-222222222222-22-22222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-222-2-22200000000000000000000000000000000000000
χ192222222-1222222-12-12-1222-12222-1-1-1-1-1-1-1-1-122-122-1-1-12-12-12-12-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000022220000-1-1-1-1-1-1-1-100000000
χ202222222-1222222-12-12-1222-12222-1-1-1-1-1-1-1-1-122-122-1-1-12-12-12-12-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000-2-2-2-200001111111100000000
χ212222222-1222222-12-12-1222-1-2-2-2-2-1-1-1-1-1-1-1-1-122-122-1-1-1-21-21-21-21-1-1-1-1111111110000000000000022-2-20000-1-1-1-1111100000000
χ222222222-1222222-12-12-1222-1-2-2-2-2-1-1-1-1-1-1-1-1-122-122-1-1-1-21-21-21-21-1-1-1-11111111100000000000000-2-22200001111-1-1-1-100000000
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χ252222222-1-2-2-2-222-12-12-1222-1-22-22-1-1-1-1-1-1-1-1-1-2-21-2-2111-212-1-212-1111111-1-111-1-100000000000000000000003−33−3−33−3300000000
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χ28222222-122222-1-12-12-12-1-1-1-1222222-1-1-1-1-1-1-1-1-12-1-1222-12-12-12-12-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2000011110000000000000000
χ29222222-122222-1-12-12-12-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-12-1-12221-21-21-21-2-1-1-1-1111111112222-1-1-1-1-1-1-1-1-2-2000011110000000000000000
χ30222222-122222-1-12-12-12-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-12-1-12221-21-21-21-2-1-1-1-111111111-2-2-2-211111111220000-1-1-1-10000000000000000
χ31222222-12-2-2-2-2-1-12-12-12-1-1-1-12-22-222-1-1-1-1-1-1-111-211-2-2-2-121-2-121-21111-1-111-1-1110000−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i30000000000000000
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χ352222-2-2222-2-22-2-222222-2-2220000-2-2-2-22-2-2222-222-2-2-22000000002-22-20000000000000000000000000000000000000022-2-20000
χ362222-2-2222-2-22-2-222222-2-2220000-2-2-2-22-2-2222-222-2-2-22000000002-22-200000000000000000000000000000000000000-2-2220000
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χ4222-2-22-222-2-22222-222-2-2-2-2-220000-22-2-2-2222-2-22-22-2-22200000000-222-2000000000000000000000000000000000000000000−2i2i2i−2i
χ4322-2-2-2222-22-22-2-2-222-2-222-222i−2i−2i2i2-222-2-2-22-2-2-2-2222-222i2i−2i−2i−2i−2i2i2i-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000
χ4422-2-2-2222-22-22-2-2-222-2-222-22−2i2i2i−2i2-222-2-2-22-2-2-2-2222-22−2i−2i2i2i2i2i−2i−2i-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000
χ4522-2-2-222-12-22-2-2-212-1-2122-2-12i2i−2i−2i-11-1-1111-1122-1-2-21-112i−i2i−i−2ii−2ii-1-111−i−i−i−iiiii000000000000002-22i−2i0000-1-111−i−iii00000000
χ4622-2-2-222-12-22-2-2-212-1-2122-2-12i2i−2i−2i-11-1-1111-1122-1-2-21-112i−i2i−i−2ii−2ii-1-111−i−i−i−iiiii00000000000000-22−2i2i000011-1-1ii−i−i00000000
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χ4822-2-2-222-12-22-2-2-212-1-2122-2-1−2i−2i2i2i-11-1-1111-1122-1-2-21-11−2ii−2ii2i−i2i−i-1-111iiii−i−i−i−i00000000000000-222i−2i000011-1-1−i−iii00000000
χ4922-2-2-222-1-22-22-2-212-1-2122-2-12i−2i−2i2i-11-1-1111-11-2-2122-11-12i−i−2ii−2ii2i−i11-1-1−i−iiiii−i−i00000000000000000000003−3−33i3−i3−i3i300000000
χ5022-2-2-222-1-22-22-2-212-1-2122-2-12i−2i−2i2i-11-1-1111-11-2-2122-11-12i−i−2ii−2ii2i−i11-1-1−i−iiiii−i−i0000000000000000000000−333−3−i3i3i3−i300000000
χ5122-2-2-222-1-22-22-2-212-1-2122-2-1−2i2i2i−2i-11-1-1111-11-2-2122-11-1−2ii2i−i2i−i−2ii11-1-1ii−i−i−i−iii00000000000000000000003−3−33−i3i3i3−i300000000
χ5222-2-2-222-1-22-22-2-212-1-2122-2-1−2i2i2i−2i-11-1-1111-11-2-2122-11-1−2ii2i−i2i−i−2ii11-1-1ii−i−i−i−iii0000000000000000000000−333−3i3−i3−i3i300000000
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χ5422-2-2-22-122-22-211-2-121-2-1-11-12i2i−2i−2i2-2-1-1111-11-1-1211-22-2−i2i−i2ii−2ii−2i-1-111−i−i−i−iiiii-2-2221111-1-1-1-1−2i2i0000ii−i−i0000000000000000
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χ904-44-400-2400002i3−2i3-42-4-242i3−2i32-20000002i3−2i322i3−2i32-20000000000000000000000000000−2i2i−2i2i−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ914-4-4400440000004-4-4-4-4004400000000400-4-400000000000000000000000000002i−2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ924-4-4400440000004-4-4-4-4004400000000400-4-40000000000000000000000000000−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ934-4-4400-240000−2i32i342-42-42i3−2i3-2-20000002i3−2i3-2−2i32i32200000000000000000000000000002i−2i−2i2i2ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ944-4-4400-240000−2i32i342-42-42i3−2i3-2-20000002i3−2i3-2−2i32i3220000000000000000000000000000−2i2i2i−2i−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ954-4-4400-2400002i3−2i342-42-4−2i32i3-2-2000000−2i32i3-22i3−2i32200000000000000000000000000002i−2i−2i2i2ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ964-4-4400-2400002i3−2i342-42-4−2i32i3-2-2000000−2i32i3-22i3−2i3220000000000000000000000000000−2i2i2i−2i−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ978-88-8008-40000004-848-400-8-4000000004004-4000000000000000000000000000000000000000000000000000000000000000000
χ988-88-800-4-40000−4i34i3444-4-4−4i34i3420000002i3−2i3-22i3−2i3-22000000000000000000000000000000000000000000000000000000000000000000
χ998-88-800-4-400004i3−4i3444-4-44i3−4i342000000−2i32i3-2−2i32i3-22000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88008-4000000-4-84-84008-400000000-40044000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-8800-4-40000−4i34i3-444444i3−4i3-42000000−2i32i322i3−2i3-2-2000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-8800-4-400004i3−4i3-44444−4i34i3-420000002i3−2i32−2i32i3-2-2000000000000000000000000000000000000000000000000000000000000000000

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