Finite Group Databasebeta

← Group #10705311

Character table — Group #10705311

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order122222344444444666888888881212121244668888121212121212121212122424242424242424242424242424242416161616161616161616161616161616444412121212121212128888
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
χ51111111-1-11111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-11111-1-1-1-1ii−i−i
χ61111111-1-11111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-11111−i−iii
χ71111111-1-11111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-11111-1-1-1-1−i−iii
χ81111111-1-11111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-1-11111ii−i−i
χ91111-1-1111-1-11111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-11-11-1
χ101111-1-1111-1-11111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-11-11
χ111111-1-1111-1-11111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-111-1-111-1-1-11-11
χ121111-1-1111-1-11111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-1-111-1-1111-11-1
χ131111-1-11-1-1-1-111-1-11111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111i−i−ii
χ141111-1-11-1-1-1-111-1-11111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-111-1-1-11111-1-1−iii−i
χ151111-1-11-1-1-1-111-1-11111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111−iii−i
χ161111-1-11-1-1-1-111-1-11111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111−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
χ18222222222-2-2-2-2-2-22220000000022222-222000022-2-2-2-2-2-2-2-20000000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ19222222222-2-2-2-2-2-22220000000022222-222000022-2-2-2-2-2-2-2-20000000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ202222222-2-22222-2-222222222222-2-2-2-2-2-222-2-2-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ212222222-2-2-2-2-2-22222200000000-2-2-2-2-22220000-2-2-2-22222-2-2000000000000000022−2−222−2−2−2−222−2−2220000000000000000
χ222222222-2-2-2-2-2-22222200000000-2-2-2-2-22220000-2-2-2-22222-2-20000000000000000−2−222−2−22222−2−222−2−20000000000000000
χ23222222-122222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ24222222-122222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ25222222-122222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ26222222-122222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ27222222-1-2-22222-2-2-1-1-1222222221111-2-2-1-1-2-2-2-211-1-11111-1-111111111-1-1-1-1-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ28222222-1-2-22222-2-2-1-1-1222222221111-2-2-1-1-2-2-2-211-1-11111-1-111111111-1-1-1-1-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ29222222-1-2-22222-2-2-1-1-1-2-2-2-2-2-2-2-21111-2-2-1-1222211-1-11111-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-111110000
χ30222222-1-2-22222-2-2-1-1-1-2-2-2-2-2-2-2-21111-2-2-1-1222211-1-11111-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-10000
χ312222-2-222222-2-2-2-2222000000002222-22-2-20000-2-222-2-222-2-20000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ322222-2-222222-2-2-2-2222000000002222-22-2-20000-2-222-2-222-2-20000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ332222-2-2222-2-222222222222-2-2-2-22222-2-2-2-2-2-222-2-2-2-222-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ342222-2-22-2-222-2-22222200000000-2-2-2-22-2-2-20000222222-2-2-2-2000000000000000022−2−2−2−222−2−22222−2−20000000000000000
χ352222-2-22-2-222-2-22222200000000-2-2-2-22-2-2-20000222222-2-2-2-20000000000000000−2−22222−2−222−2−2−2−2220000000000000000
χ362222-2-22-2-2-2-222-2-2222-2-2-2-22222-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ372222-2-2-122-2-22222-1-1-12222-2-2-2-2-1-1-1-1-2-211-2-2221111-1-111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ382222-2-2-122-2-22222-1-1-12222-2-2-2-2-1-1-1-1-2-211-2-2221111-1-111-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ392222-2-2-122-2-22222-1-1-1-2-2-2-22222-1-1-1-1-2-21122-2-21111-1-111-1-1-1-1-1-11111-1-1-1-1111100000000000000002-22-2-1-111-1-1110000
χ402222-2-2-122-2-22222-1-1-1-2-2-2-22222-1-1-1-1-2-21122-2-21111-1-111-1-1-1-1-1-11111-1-1-1-111110000000000000000-22-2211-1-111-1-10000
χ412222-2-2-1-2-2-2-222-2-2-1-1-12222-2-2-2-21111221122-2-2-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000002-2-22-1-11111-1-10000
χ422222-2-2-1-2-2-2-222-2-2-1-1-12222-2-2-2-21111221122-2-2-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000-222-211-1-1-1-1110000
χ432222-2-2-1-2-2-2-222-2-2-1-1-1-2-2-2-2222211112211-2-222-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ442222-2-2-1-2-2-2-222-2-2-1-1-1-2-2-2-2222211112211-2-222-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ452-22-20022i−2i002-22i−2i-22-200002i2i−2i−2i2i2i−2i−2i00002-20000002i−2i002-222-2-200002i2i−2i−2i000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ462-22-20022i−2i002-22i−2i-22-200002i2i−2i−2i2i2i−2i−2i00002-20000002i−2i002-222-2-200002i2i−2i−2i00000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ472-22-20022i−2i002-22i−2i-22-20000−2i−2i2i2i2i2i−2i−2i0000-220000002i−2i002-2-2-2220000−2i−2i2i2i0000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ482-22-20022i−2i002-22i−2i-22-20000−2i−2i2i2i2i2i−2i−2i0000-220000002i−2i002-2-2-2220000−2i−2i2i2i00002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ492-22-20022i−2i00-22−2i2i-22-222-2-200002i2i−2i−2i0000002i−2i0000−2i2i00-2200002i2i−2i−2i000022-2-21+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ502-22-20022i−2i00-22−2i2i-22-222-2-200002i2i−2i−2i0000002i−2i0000−2i2i00-2200002i2i−2i−2i000022-2-2−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ512-22-20022i−2i00-22−2i2i-22-2-2-22200002i2i−2i−2i000000−2i2i0000−2i2i00-220000−2i−2i2i2i0000-2-2221+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ522-22-20022i−2i00-22−2i2i-22-2-2-22200002i2i−2i−2i000000−2i2i0000−2i2i00-220000−2i−2i2i2i0000-2-222−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ532-22-2002−2i2i002-2−2i2i-22-200002i2i−2i−2i−2i−2i2i2i0000-22000000−2i2i002-2-2-22200002i2i−2i−2i00002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ542-22-2002−2i2i002-2−2i2i-22-200002i2i−2i−2i−2i−2i2i2i0000-22000000−2i2i002-2-2-22200002i2i−2i−2i0000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ552-22-2002−2i2i002-2−2i2i-22-20000−2i−2i2i2i−2i−2i2i2i00002-2000000−2i2i002-222-2-20000−2i−2i2i2i00000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ562-22-2002−2i2i002-2−2i2i-22-20000−2i−2i2i2i−2i−2i2i2i00002-2000000−2i2i002-222-2-20000−2i−2i2i2i000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ572-22-2002−2i2i00-222i−2i-22-222-2-20000−2i−2i2i2i000000−2i2i00002i−2i00-220000−2i−2i2i2i000022-2-21−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ582-22-2002−2i2i00-222i−2i-22-222-2-20000−2i−2i2i2i000000−2i2i00002i−2i00-220000−2i−2i2i2i000022-2-2−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
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χ602-22-2002−2i2i00-222i−2i-22-2-2-2220000−2i−2i2i2i0000002i−2i00002i−2i00-2200002i2i−2i−2i0000-2-222−1+i1−i1−i−1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ61444444-244-4-4-4-4-4-4-2-2-200000000-2-2-2-24-4-2-20000-2-222222222000000000000000000000000000000000000000000000000
χ62444444-2-4-4-4-4-4-444-2-2-2000000002222-44-2-200002222-2-2-2-222000000000000000000000000000000000000000000000000
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χ6544-4-44-44000000004-4-422−2222−2222−2222−220000004-4000000000000000000000022−2222−2222−2222−2200000000000000000000000000000000
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χ7144-4-4-444000000004-4-422−2222−22−2222−2222000000-440000000000000000000000−2222−222222−2222−2200000000000000000000000000000000
χ7244-4-4-444000000004-4-4−2222−222222−2222−22000000-44000000000000000000000022−2222−22−2222−222200000000000000000000000000000000
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χ7444-4-4-44-200000000-22222−2222−22−2222−22222i3−2i32i3−2i3002-20000−2i32i300000000i6−i6i6−i6−i6i6−i6i62−22−2−22−2200000000000000000000000000000000
χ7544-4-4-44-200000000-222−2222−222222−2222−22−2i32i3−2i32i3002-200002i3−2i300000000i6−i6i6−i6−i6i6−i6i6−22−222−22−200000000000000000000000000000000
χ7644-4-4-44-200000000-222−2222−222222−2222−222i3−2i32i3−2i3002-20000−2i32i300000000−i6i6−i6i6i6−i6i6−i6−22−222−22−200000000000000000000000000000000
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χ794-44-400-24i−4i00-44−4i4i2-2244-4-40000−2i−2i2i2i0000004i−4i00002i−2i002-20000−2i−2i2i2i0000-2-22200000000000000000000000000000000
χ804-44-400-24i−4i00-44−4i4i2-22-4-4440000−2i−2i2i2i000000−4i4i00002i−2i002-200002i2i−2i−2i000022-2-200000000000000000000000000000000
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χ824-44-400-2−4i4i004-4−4i4i2-220000−4i−4i4i4i2i2i−2i−2i00004-40000002i−2i00-22-2-22200002i2i−2i−2i000000000000000000000000000000000000
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χ874-4-4400400−4i4i0000-4-4422−22−22222i2−2i2−2i22i200000000000000−4i4i000000000000002i2−2i2−2i22i222−22−222200000000000000000000000000000000
χ884-4-4400400−4i4i0000-4-44−222222−22−2i22i22i2−2i200000000000000−4i4i00000000000000−2i22i22i2−2i2−222222−2200000000000000000000000000000000
χ894-4-4400-2004i−4i000022-222−22−2222−2i22i22i2−2i223−23−23230000000000−2i2i00−2i32i300−i6i6i6−i6−666−6i2−i2−i2i2−222−200000000000000000000000000000000
χ904-4-4400-2004i−4i000022-222−22−2222−2i22i22i2−2i2−232323−230000000000−2i2i002i3−2i300i6−i6−i6i66−6−66i2−i2−i2i2−222−200000000000000000000000000000000
χ914-4-4400-2004i−4i000022-2−222222−222i2−2i2−2i22i223−23−23230000000000−2i2i00−2i32i300i6−i6−i6i66−6−66−i2i2i2−i22−2−2200000000000000000000000000000000
χ924-4-4400-2004i−4i000022-2−222222−222i2−2i2−2i22i2−232323−230000000000−2i2i002i3−2i300−i6i6i6−i6−666−6−i2i2i2−i22−2−2200000000000000000000000000000000
χ934-4-4400-200−4i4i000022-222−22−22222i2−2i2−2i22i223−23−232300000000002i−2i002i3−2i300i6−i6−i6i6−666−6−i2i2i2−i2−222−200000000000000000000000000000000
χ944-4-4400-200−4i4i000022-222−22−22222i2−2i2−2i22i2−232323−2300000000002i−2i00−2i32i300−i6i6i6−i66−6−66−i2i2i2−i2−222−200000000000000000000000000000000
χ954-4-4400-200−4i4i000022-2−222222−22−2i22i22i2−2i223−23−232300000000002i−2i002i3−2i300−i6i6i6−i66−6−66i2−i2−i2i22−2−2200000000000000000000000000000000
χ964-4-4400-200−4i4i000022-2−222222−22−2i22i22i2−2i2−232323−2300000000002i−2i00−2i32i300i6−i6−i6i6−666−6i2−i2−i2i22−2−2200000000000000000000000000000000

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