Finite Group Databasebeta

← Group #11782834

Character table — Group #11782834

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11112222222222222244444444444444444444444444444444444444444444444444444444444444443636363636363636484848484848484848484848
order12223344444466666636668888121212121212121212121212121212121212121212121212242424242424242424242424242424242424242424242424242424242424242488888888244466121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-11-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-11111
χ51111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ61111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ71111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111
χ81111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1
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χ824-44-4-2-2-4400002-22-22211-1-14i−4i0000000000−3i3i−3i3i3i−3i3i−3i2-22-2-1-111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i0000000033-3-3-3-33300000000000000000000
χ834-44-4-2-2-4400002-22-22211-1-1−4i4i00000000003i−3i3i−3i−3i3i−3i3i2-22-2-1-1112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii0000000033-3-3-3-33300000000000000000000
χ844-44-4-2-2-4400002-22-22211-1-1−4i4i0000000000−3i3i−3i3i3i−3i3i−3i2-22-2-1-1112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii00000000-3-33333-3-300000000000000000000
χ854-4-444400004-4-4-4-4-4444-4-44000000004-44-400004-4-44000000000000000000000000000000000000000000000000000000000000
χ864-4-44440000-44-4-4-4-4444-4-4400000000-44-440000-444-4000000000000000000000000000000000000000000000000000000000000
χ874-4-444-200004-4-422-44-2-222-2000000004-4-220000-222-2000000000000i6−i6−i6i6i6−i6i6−i6−i6i6−i6i60000i6−i6−i6i6i6−i6i6−i6−i6i6−i6i600000000000000000000
χ884-4-444-200004-4-422-44-2-222-2000000004-4-220000-222-2000000000000−i6i6i6−i6−i6i6−i6i6i6−i6i6−i60000−i6i6i6−i6−i6i6−i6i6i6−i6i6−i600000000000000000000
χ894-4-444-20000-44-422-44-2-222-200000000-442-200002-2-22000000000000i6−i6−i6i6i6−i6i6−i6−i6i6−i6i60000−i6i6i6−i6−i6i6−i6i6i6−i6i6−i600000000000000000000
χ904-4-444-20000-44-422-44-2-222-200000000-442-200002-2-22000000000000−i6i6i6−i6−i6i6−i6i6i6−i6i6−i60000i6−i6−i6i6i6−i6i6−i6−i6i6−i6i600000000000000000000
χ914-4-44-2400004-42-4-42-24-222-200000000-224-40000-222-2000000006−6−6600006−6−66−666−6−666−60000−666−66−6−6600000000000000000000
χ924-4-44-2400004-42-4-42-24-222-200000000-224-40000-222-200000000−666−60000−666−66−6−666−6−6600006−6−66−666−600000000000000000000
χ934-4-44-240000-442-4-42-24-222-2000000002-2-4400002-2-22000000006−6−6600006−6−66−666−66−6−6600006−6−66−666−600000000000000000000
χ944-4-44-240000-442-4-42-24-222-2000000002-2-4400002-2-2200000000−666−60000−666−66−6−66−666−60000−666−66−6−6600000000000000000000
χ954-4-44-2-200004-42222-2-21-1-1100000000-22-223i−3i−3i3i1-1-110000−3i3i3i−3i6−6−66−i6i6i6−i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−666−6−i6i6i6−i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ2300000000000000000000
χ964-4-44-2-200004-42222-2-21-1-1100000000-22-223i−3i−3i3i1-1-110000−3i3i3i−3i−666−6i6−i6−i6i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ136−6−66i6−i6−i6i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ2300000000000000000000
χ974-4-44-2-200004-42222-2-21-1-1100000000-22-22−3i3i3i−3i1-1-1100003i−3i−3i3i6−6−66i6−i6−i6i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−666−6i6−i6−i6i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ1300000000000000000000
χ984-4-44-2-200004-42222-2-21-1-1100000000-22-22−3i3i3i−3i1-1-1100003i−3i−3i3i−666−6−i6i6i6−i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ236−6−66−i6i6i6−i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ1300000000000000000000
χ994-4-44-2-20000-442222-2-21-1-11000000002-22-23i−3i−3i3i-111-100003i−3i−3i3i6−6−66i6−i6−i6i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ236−6−66−i6i6i6−i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ1300000000000000000000
χ1004-4-44-2-20000-442222-2-21-1-11000000002-22-23i−3i−3i3i-111-100003i−3i−3i3i−666−6−i6i6i6−i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−666−6i6−i6−i6i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ1300000000000000000000
χ1014-4-44-2-20000-442222-2-21-1-11000000002-22-2−3i3i3i−3i-111-10000−3i3i3i−3i6−6−66−i6i6i6−i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ136−6−66i6−i6−i6i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ2300000000000000000000
χ1024-4-44-2-20000-442222-2-21-1-11000000002-22-2−3i3i3i−3i-111-10000−3i3i3i−3i−666−6i6−i6−i6i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−666−6−i6i6i6−i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ2300000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.