Finite Group Databasebeta

← Group #10691287

Character table — Group #10691287

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order12224444223444444666121212124466888888881212121212121212121224242424242424242424242424242424448812121212242424242444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ91111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1iiii−i−i−i−i111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1i−i11-1-1ii−i−i1-11-1ii−i−iii−i−i11-1-1
χ101111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1iiii−i−i−i−i111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1i−i11-1-1ii−i−i-11-11−i−iii−i−iii-1-111
χ111111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1iiii−i−i−i−i111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11−ii-1-111−i−iii1-11-1−i−iiiii−i−i-1-111
χ121111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1iiii−i−i−i−i111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11−ii-1-111−i−iii-11-11ii−i−i−i−iii11-1-1
χ131111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1−ii11-1-1−i−iii1-11-1−i−iii−i−iii11-1-1
χ141111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1−ii11-1-1−i−iii-11-11ii−i−iii−i−i-1-111
χ151111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11i−i-1-111ii−i−i1-11-1ii−i−i−i−iii-1-111
χ161111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11i−i-1-111ii−i−i-11-11−i−iiiii−i−i11-1-1
χ17222222222222-2-2-2-222222222-2-2220000000022-2-2-2-2-2-2-2-2000000000000000000000000000022-2-2000000000000
χ18222222222222-2-2-2-222222222-2-2220000000022-2-2-2-2-2-2-2-20000000000000000000000000000-2-222000000000000
χ192222222222-1222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ202222222222-1222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ212222222222-1222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-111110000000000000000
χ222222222222-1222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-10000000000000000
χ2322222222-2-22-22222-22222222-2-2-2-222-2-222-2-2-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ2422222222-2-22-22222-22222222-2-2-2-2-2-222-2-222-2-222-2-2-2-222-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ2522222222-2-22-2-2-2-2-2-2222222222-2-200000000-2-2-2-22222-2-20000000000000000000000000000000000002i−2i2i−2i0000
χ2622222222-2-22-2-2-2-2-2-2222222222-2-200000000-2-2-2-22222-2-2000000000000000000000000000000000000−2i2i−2i2i0000
χ2722222222-2-2-1-22222-2-1-1-1-1-1-1-1-2-21122-2-222-2-211-1-11111-1-1-1-1-1-11111-1-1-1-111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2822222222-2-2-1-22222-2-1-1-1-1-1-1-1-2-21122-2-222-2-211-1-11111-1-1-1-1-1-11111-1-1-1-111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2922222222-2-2-1-22222-2-1-1-1-1-1-1-1-2-211-2-222-2-22211-1-11111-1-11111-1-1-1-11111-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ3022222222-2-2-1-22222-2-1-1-1-1-1-1-1-2-211-2-222-2-22211-1-11111-1-11111-1-1-1-11111-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
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χ322222-2-2-2-2222-222-2-2-2222-2-2-2-2-2222−2i−2i2i2i2i2i−2i−2i-2-222-2-222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000
χ332222-2-2-2-2222-2-2-222-2222-2-2-2-22-22200000000-2-2-2-222-2-2220000000000000000000000000000000000002-2-220000
χ342222-2-2-2-2222-2-2-222-2222-2-2-2-22-22200000000-2-2-2-222-2-222000000000000000000000000000000000000-222-20000
χ352222-2-2-2-222-1-222-2-2-2-1-1-11111-22-1-12i2i−2i−2i−2i−2i2i2i11-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i0000−i3i3i3−i33−3−330000000000000000
χ362222-2-2-2-222-1-222-2-2-2-1-1-11111-22-1-12i2i−2i−2i−2i−2i2i2i11-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i0000i3−i3−i3i3−333−30000000000000000
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χ392222-2-2-2-2-2-222-2-2222222-2-2-2-2-22-2-20000000022-2-2-2-2222200000000000000000000000000002-2-22000000000000
χ402222-2-2-2-2-2-222-2-2222222-2-2-2-2-22-2-20000000022-2-2-2-222220000000000000000000000000000-222-2000000000000
χ412222-2-2-2-2-2-2-1222-2-22-1-1-111112-2112i2i2i2i−2i−2i−2i−2i-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii2-22i−2i-1-111−i−iii0000000000000000
χ422222-2-2-2-2-2-2-1222-2-22-1-1-111112-2112i2i2i2i−2i−2i−2i−2i-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-22−2i2i11-1-1ii−i−i0000000000000000
χ432222-2-2-2-2-2-2-1222-2-22-1-1-111112-211−2i−2i−2i−2i2i2i2i2i-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i2-2−2i2i-1-111ii−i−i0000000000000000
χ442222-2-2-2-2-2-2-1222-2-22-1-1-111112-211−2i−2i−2i−2i2i2i2i2i-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-222i−2i11-1-1−i−iii0000000000000000
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χ462-22-22i−2i2i−2i00202-22i−2i0-22-22i−2i2i−2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23002-200002i−2i0000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ230000000000000000−1+i1−i−1−i1+i0000−22i2−i2
χ472-22-22i−2i2i−2i00202-22i−2i0-22-22i−2i2i−2i0000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23002-200002i−2i00002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2300000000000000001−i−1+i1+i−1−i0000−22i2−i2
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χ492-22-2−2i2i−2i2i00202-2−2i2i0-22-2−2i2i−2i2i0000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13002-20000−2i2i00002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ230000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300000000000000001+i−1−i1−i−1+i00002−2i2−i2
χ502-22-2−2i2i−2i2i00202-2−2i2i0-22-2−2i2i−2i2i0000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13002-20000−2i2i00002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ230000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ130000000000000000−1−i1+i−1+i1−i0000−22−i2i2
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χ534444444444-24-4-4-4-44-2-2-2-2-2-2-2-4-4-2-200000000-2-22222222200000000000000000000000000000000000000000000
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χ824-4-444i−4i−4i4i00-200000022-2−2i2i2i−2i00002−2i−2+2i002+2i−2−2i0000002i3−2i3−232300−1+i1−i1−i−1+iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ221+i−1−i−1−i1+iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000000000000000000000
χ834-4-444i−4i−4i4i00-200000022-2−2i2i2i−2i0000−2+2i2−2i00−2−2i2+2i000000−2i32i323−23001−i−1+i−1+i1−iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−1−i1+i1+i−1−iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000000000000000000000
χ844-4-444i−4i−4i4i00-200000022-2−2i2i2i−2i0000−2+2i2−2i00−2−2i2+2i0000002i3−2i3−2323001−i−1+i−1+i1−i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−1−i1+i1+i−1−i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ220000000000000000000000000000
χ854-4-44−4i4i4i−4i004000000-4-44−4i4i4i−4i00002+2i−2−2i002−2i−2+2i0000000000002+2i−2−2i−2−2i2+2i0000−2+2i2−2i2−2i−2+2i00000000000000000000000000000000
χ864-4-44−4i4i4i−4i004000000-4-44−4i4i4i−4i0000−2−2i2+2i00−2+2i2−2i000000000000−2−2i2+2i2+2i−2−2i00002−2i−2+2i−2+2i2−2i00000000000000000000000000000000
χ874-4-44−4i4i4i−4i00-200000022-22i−2i−2i2i00002+2i−2−2i002−2i−2+2i000000−2i32i3−232300−1−i1+i1+i−1−i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ221−i−1+i−1+i1−i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000000000000000000000
χ884-4-44−4i4i4i−4i00-200000022-22i−2i−2i2i00002+2i−2−2i002−2i−2+2i0000002i3−2i323−2300−1−i1+i1+i−1−iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ221−i−1+i−1+i1−iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000000000000000000000
χ894-4-44−4i4i4i−4i00-200000022-22i−2i−2i2i0000−2−2i2+2i00−2+2i2−2i000000−2i32i3−2323001+i−1−i−1−i1+iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−1+i1−i1−i−1+iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000000000000000000000
χ904-4-44−4i4i4i−4i00-200000022-22i−2i−2i2i0000−2−2i2+2i00−2+2i2−2i0000002i3−2i323−23001+i−1−i−1−i1+i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−1+i1−i1−i−1+i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000000000000000000000

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