Finite Group Databasebeta

← Group #10693637

Character table — Group #10693637

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order122244442234444446661212121244444444446612121212121212121212121212121212121212121212121212122466881212242424248888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111
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χ101111-1-1-1-1-1-11111-1-11111-1-1-1-11-1iiii−i−i−i−i-1-11111-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i1-111i−i-1-1ii−i−i−i−iii−i−iii-1-111-1-111
χ111111-1-1-1-1-1-11111-1-11111-1-1-1-11-1iiii−i−i−i−i-1-11111-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i-11-1-1−ii11−i−iiiii−i−i−i−iii-1-11111-1-1
χ121111-1-1-1-1-1-11111-1-11111-1-1-1-11-1iiii−i−i−i−i-1-11111-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i-11-1-1−ii11−i−iii−i−iiiii−i−i11-1-1-1-111
χ131111-1-1-1-1-1-11111-1-11111-1-1-1-11-1−i−i−i−iiiii-1-11111-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii1-111−ii-1-1−i−iiiii−i−iii−i−i-1-111-1-111
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χ151111-1-1-1-1-1-11111-1-11111-1-1-1-11-1−i−i−i−iiiii-1-11111-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii-11-1-1i−i11ii−i−iii−i−i−i−iii11-1-1-1-111
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χ192222222222-1222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-10000000000000000
χ202222222222-1222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-21111110000000000000000
χ212222222222-1222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-1-1-2-2-1-111110000000000000000
χ222222222222-1222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2112211-1-1-1-10000000000000000
χ232222222222-12-2-2-2-22-1-1-1-1-1-1-1-2-222-2-222-2-2-1-111111111-1-1-1-1-1-11111-1-1-1-1111100−i3i300−i3i3−i3i3−i3i30000000000000000
χ242222222222-12-2-2-2-22-1-1-1-1-1-1-1-2-222-2-222-2-2-1-111111111-1-1-1-1-1-11111-1-1-1-1111100i3−i300i3−i3i3−i3i3−i30000000000000000
χ252222222222-12-2-2-2-22-1-1-1-1-1-1-1-2-2-2-222-2-222-1-111111111-1-11111-1-1-1-11111-1-1-1-100−i3i300−i3i3i3−i3i3−i30000000000000000
χ262222222222-12-2-2-2-22-1-1-1-1-1-1-1-2-2-2-222-2-222-1-111111111-1-11111-1-1-1-11111-1-1-1-100i3−i300i3−i3−i3i3−i3i30000000000000000
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χ352222-2-2-2-2-2-222-2-2222222-2-2-2-2-222i2i−2i−2i−2i−2i2i2i-2-2-2-2-2-22222222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000
χ362222-2-2-2-2-2-222-2-2222222-2-2-2-2-22−2i−2i2i2i2i2i−2i−2i-2-2-2-2-2-2222222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000
χ372222-2-2-2-2-2-2-1222-2-22-1-1-111112-22i2i2i2i−2i−2i−2i−2i11-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii2-2-1-12i−2i11−i−iii0000000000000000
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χ784-44-4−4i4i4i−4i00-204-4−4i4i02-222i−2i−2i2i000000000000-22002i−2i0000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000000000000000000000
χ794-44-4−4i4i4i−4i00-20-444i−4i02-222i−2i−2i2i0000000000002-200−2i2i0000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000000000000000000000
χ804-44-4−4i4i4i−4i00-20-444i−4i02-222i−2i−2i2i0000000000002-200−2i2i0000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000000000000000000000
χ814-4-4444-4-44-4-2-40000422-2-2-22200004i−4i004i−4i-2200000000-220000−2i−2i2i2i0000−2i−2i2i2i0000000000000000000000000000
χ824-4-4444-4-44-4-2-40000422-2-2-2220000−4i4i00−4i4i-2200000000-2200002i2i−2i−2i00002i2i−2i−2i0000000000000000000000000000
χ834-4-4444-4-4-44440000-4-4-4444-4-40000000000-4400000000-4400000000000000000000000000000000000000000000
χ844-4-4444-4-4-44-240000-422-2-2-22200000000002-2000000002-223−23−23230000−232323−2300000000000000000000000000000000
χ854-4-4444-4-4-44-240000-422-2-2-22200000000002-2000000002-2−232323−23000023−23−232300000000000000000000000000000000
χ864-4-44-4-4444-4440000-4-4-44-4-44400000000004-400000000-4400000000000000000000000000000000000000000000
χ874-4-44-4-4444-4-240000-422-222-2-20000000000-22000000002-2−2i32i32i3−2i30000−2i32i32i3−2i300000000000000000000000000000000
χ884-4-44-4-4444-4-240000-422-222-2-20000000000-22000000002-22i3−2i3−2i32i300002i3−2i3−2i32i300000000000000000000000000000000
χ894-4-44-4-444-44-2-40000422-222-2-200004-400-442-200000000-220000-2-222000022-2-20000000000000000000000000000
χ904-4-44-4-444-44-2-40000422-222-2-20000-44004-42-200000000-22000022-2-20000-2-2220000000000000000000000000000

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