Finite Group Databasebeta

← Group #10705315

Character table — Group #10705315

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order12223444444444466688888888121212122466888812121212121212121212242424242424242424242424242424241616161616161616161616161616161622446666121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-11111-1-1-1-1ii−i−i
χ6111111111-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-11111−i−iii
χ7111111111-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-11111-1-1-1-1−i−iii
χ8111111111-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-1-11111ii−i−i
χ911111-1-1-1-1111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-11-11-1
χ1011111-1-1-1-1111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-11-11
χ1111111-1-1-1-1111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-111-1-111-1-1-11-11
χ1211111-1-1-1-1111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-1-111-1-1111-11-1
χ1311111-1-1-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111i−i−ii
χ1411111-1-1-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-111-1-1-11111-1-1−iii−i
χ1511111-1-1-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111−iii−i
χ1611111-1-1-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-11111-1-1i−i−ii
χ17222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222-2-222-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ192222222-2-222-2-2-2-2222000000002222-22-2-2000022-2-222-2-2-2-20000000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ202222222-2-222-2-2-2-2222000000002222-22-2-2000022-2-222-2-2-2-20000000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ212222222-2-2-2-2-2-22222200000000-2-2-2-22-22200002222-2-2-2-2-2-2000000000000000022−2−222−2−2−2−222−2−2220000000000000000
χ222222222-2-2-2-2-2-22222200000000-2-2-2-22-22200002222-2-2-2-2-2-20000000000000000−2−222−2−22222−2−222−2−20000000000000000
χ2322222-2-22222-2-2-2-22220000000022222-2220000-2-2-2-2-2-222-2-20000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ2422222-2-22222-2-2-2-22220000000022222-2220000-2-2-2-2-2-222-2-20000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ2522222-2-222-2-2-2-22222200000000-2-2-2-2-22-2-20000-2-2222222-2-2000000000000000022−2−2−2−222−2−22222−2−20000000000000000
χ2622222-2-222-2-2-2-22222200000000-2-2-2-2-22-2-20000-2-2222222-2-20000000000000000−2−22222−2−222−2−2−2−2220000000000000000
χ2722222-2-2-2-22222222222222-2-2-2-22222-2-2-2-2-2-222-2-222-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2822222-2-2-2-2-2-222-2-2222-2-2-2-22222-2-2-2-22222-2-222-2-2-2-222-2-222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ292222-12222222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ302222-12222222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ312222-12222222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ322222-12222222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ332222-12222-2-222-2-2-1-1-1222222221111-2-211-2-2-2-2-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ342222-12222-2-222-2-2-1-1-1222222221111-2-211-2-2-2-2-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ352222-12222-2-222-2-2-1-1-1-2-2-2-2-2-2-2-21111-2-2112222-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-111110000
χ362222-12222-2-222-2-2-1-1-1-2-2-2-2-2-2-2-21111-2-2112222-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-10000
χ372222-1-2-2-2-2222222-1-1-12222-2-2-2-2-1-1-1-1-2-211-2-22211-1-11111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ382222-1-2-2-2-2222222-1-1-12222-2-2-2-2-1-1-1-1-2-211-2-22211-1-11111-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ392222-1-2-2-2-2222222-1-1-1-2-2-2-22222-1-1-1-1-2-21122-2-211-1-11111-1-1-1-1-1-11111-1-1-1-1111100000000000000002-22-2-1-111-1-1110000
χ402222-1-2-2-2-2222222-1-1-1-2-2-2-22222-1-1-1-1-2-21122-2-211-1-11111-1-1-1-1-1-11111-1-1-1-111110000000000000000-22-2211-1-111-1-10000
χ412222-1-2-2-2-2-2-222-2-2-1-1-12222-2-2-2-2111122-1-122-2-21111-1-111-1-1-1-1-1-111111111-1-1-1-100000000000000002-2-22-1-11111-1-10000
χ422222-1-2-2-2-2-2-222-2-2-1-1-12222-2-2-2-2111122-1-122-2-21111-1-111-1-1-1-1-1-111111111-1-1-1-10000000000000000-222-211-1-1-1-1110000
χ432222-1-2-2-2-2-2-222-2-2-1-1-1-2-2-2-22222111122-1-1-2-2221111-1-111-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ442222-1-2-2-2-2-2-222-2-2-1-1-1-2-2-2-22222111122-1-1-2-2221111-1-111-1-11111-1-1-1-1-1-1-1-1111100000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ4522-2-2200002i−2i2-22i−2i2-2-200002i2i−2i−2i2i2i−2i−2i00002-200002i−2i00002-222-2-200002i2i−2i−2i00000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000
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χ4722-2-2200002i−2i2-22i−2i2-2-20000−2i−2i2i2i2i2i−2i−2i0000-2200002i−2i00002-2-2-2220000−2i−2i2i2i0000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ4822-2-2200002i−2i2-22i−2i2-2-20000−2i−2i2i2i2i2i−2i−2i0000-2200002i−2i00002-2-2-2220000−2i−2i2i2i00002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ4922-2-2200002i−2i-22−2i2i2-2-22i2i−2i−2i00002i2i−2i−2i0000002-200−2i2i0000-22000022-2-200002i2i−2i−2i1+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i0000000000000000
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χ5222-2-2200002i−2i-22−2i2i2-2-2−2i−2i2i2i00002i2i−2i−2i000000-2200−2i2i0000-220000-2-2220000−2i−2i2i2i−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i0000000000000000
χ5322-2-220000−2i2i2-2−2i2i2-2-200002i2i−2i−2i−2i−2i2i2i0000-220000−2i2i00002-2-2-22200002i2i−2i−2i00002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ5422-2-220000−2i2i2-2−2i2i2-2-200002i2i−2i−2i−2i−2i2i2i0000-220000−2i2i00002-2-2-22200002i2i−2i−2i0000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ5522-2-220000−2i2i2-2−2i2i2-2-20000−2i−2i2i2i−2i−2i2i2i00002-20000−2i2i00002-222-2-20000−2i−2i2i2i000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ5622-2-220000−2i2i2-2−2i2i2-2-20000−2i−2i2i2i−2i−2i2i2i00002-20000−2i2i00002-222-2-20000−2i−2i2i2i00000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ5722-2-220000−2i2i-222i−2i2-2-22i2i−2i−2i0000−2i−2i2i2i000000-22002i−2i0000-220000-2-22200002i2i−2i−2i1−i−1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i0000000000000000
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χ614444-244-4-444-4-4-4-4-2-2-200000000-2-2-2-2-44220000-2-222-2-22222000000000000000000000000000000000000000000000000
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χ7244-4-4-20000−4i4i-444i−4i-222−4i−4i4i4i00002i2i−2i−2i0000004-400−2i2i00002-20000-2-22200002i2i−2i−2i00000000000000000000000000000000
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χ784-44-4-24-4000000002-22−2i22i2−2i22i2−2i22i2−2i22i2−2323−232300000000-2200−23230000−i6i6−i6i6−i6i6−i6i6i2−i2i2−i2i2−i2i2−i200000000000000000000000000000000
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χ824-44-4-2-44000000002-22−2i22i2−2i22i22i2−2i22i2−2i2−2323−2323000000002-20023−230000i6−i6i6−i6−i6i6−i6i6−i2i2−i2i2i2−i2i2−i200000000000000000000000000000000
χ834-44-4-2-44000000002-222i2−2i22i2−2i2−2i22i2−2i22i223−2323−23000000002-200−23230000i6−i6i6−i6−i6i6−i6i6i2−i2i2−i2−i2i2−i2i200000000000000000000000000000000
χ844-44-4-2-44000000002-222i2−2i22i2−2i2−2i22i2−2i22i2−2323−2323000000002-20023−230000−i6i6−i6i6i6−i6i6−i6i2−i2i2−i2−i2i2−i2i200000000000000000000000000000000
χ854-4-444004-4000000-4-4422−22−222222−22−22220000000000000000004-4000000000022−22−222222−22−222200000000000000000000000000000000
χ864-4-444004-4000000-4-44−222222−22−222222−220000000000000000004-40000000000−222222−22−222222−2200000000000000000000000000000000
χ874-4-44400-44000000-4-4422−22−2222−222222−22000000000000000000-440000000000−222222−2222−22−222200000000000000000000000000000000
χ884-4-44400-44000000-4-44−222222−2222−22−2222000000000000000000-44000000000022−22−2222−222222−2200000000000000000000000000000000
χ894-4-44-2004-400000022-222−22−222222−22−2222−2i32i32i3−2i300−2i32i30000000000-2200−i6i6i6−i6−i6i6i6−i6−222−2−222−200000000000000000000000000000000
χ904-4-44-2004-400000022-222−22−222222−22−22222i3−2i3−2i32i3002i3−2i30000000000-2200i6−i6−i6i6i6−i6−i6i6−222−2−222−200000000000000000000000000000000
χ914-4-44-2004-400000022-2−222222−22−222222−22−2i32i32i3−2i300−2i32i30000000000-2200i6−i6−i6i6i6−i6−i6i62−2−222−2−2200000000000000000000000000000000
χ924-4-44-2004-400000022-2−222222−22−222222−222i3−2i3−2i32i3002i3−2i30000000000-2200−i6i6i6−i6−i6i6i6−i62−2−222−2−2200000000000000000000000000000000
χ934-4-44-200-4400000022-222−22−2222−222222−22−2i32i32i3−2i3002i3−2i300000000002-200i6−i6−i6i6−i6i6i6−i62−2−22−222−200000000000000000000000000000000
χ944-4-44-200-4400000022-222−22−2222−222222−222i3−2i3−2i32i300−2i32i300000000002-200−i6i6i6−i6i6−i6−i6i62−2−22−222−200000000000000000000000000000000
χ954-4-44-200-4400000022-2−222222−2222−22−2222−2i32i32i3−2i3002i3−2i300000000002-200−i6i6i6−i6i6−i6−i6i6−222−22−2−2200000000000000000000000000000000
χ964-4-44-200-4400000022-2−222222−2222−22−22222i3−2i3−2i32i300−2i32i300000000002-200i6−i6−i6i6−i6i6i6−i6−222−22−2−2200000000000000000000000000000000

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