Finite Group Databasebeta

← Group #10693706

Character table — Group #10693706

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order122244442234444446661212121244668888888812121212121288888888444412121212121212121212242424242424242488888888888824661212888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ91111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1ii−i−iii−i−i11-1-111iiii−i−i−i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i1111-1-1-1-11-111-1-111-1-1i−i
χ101111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1ii−i−iii−i−i11-1-111iiii−i−i−i−i−i−iii1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i1111-1-1-1-1-11-1-111-1-111−ii
χ111111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1ii−i−iii−i−i11-1-111−i−i−i−iiiiiii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii-1-1-1-111111-111-1-1-1-111−ii
χ121111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1ii−i−iii−i−i11-1-111−i−i−i−iiiii−i−iii1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iii-1-1-1-11111-11-1-11111-1-1i−i
χ131111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1−i−iii−i−iii11-1-111iiii−i−i−i−iii−i−i1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i-1-1-1-11111-11-1-11111-1-1−ii
χ141111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1−i−iii−i−iii11-1-111iiii−i−i−i−i−i−iii1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-1-1-111111-111-1-1-1-111i−i
χ151111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1−i−iii−i−iii11-1-111−i−i−i−iiiiiii−i−i1-1iiii−i−i−i−i−i−i−i−iiiii−i−iii1111-1-1-1-1-11-1-111-1-111i−i
χ161111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1−i−iii−i−iii11-1-111−i−i−i−iiiii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii1111-1-1-1-11-111-1-111-1-1−ii
χ17222222222222-2-2-2-222222222-2-2222222-2-2-2-2-2-2-2-222000000000000-2-20000000022-2-222-2-2000000000000000000000000
χ18222222222222-2-2-2-222222222-2-222-2-2-2-22222-2-2-2-222000000000000-2-200000000-2-222-2-222000000000000000000000000
χ192222222222-1222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ202222222222-1222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-100000000-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ212222222222-1222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ222222222222-1222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-100000000-2-2-2-2-1-1111111111111111100000000000022-1-1-1-1000000
χ232222222222-12-2-2-2-22-1-1-1-1-1-1-1-2-2-1-12222-2-2-2-21111-1-100000000000011−i3−i3i3i3−i3−i3i3i3-1-111-1-11100000000000000−i3i3−i3i3000000
χ242222222222-12-2-2-2-22-1-1-1-1-1-1-1-2-2-1-12222-2-2-2-21111-1-100000000000011i3i3−i3−i3i3i3−i3−i3-1-111-1-11100000000000000i3−i3i3−i3000000
χ252222222222-12-2-2-2-22-1-1-1-1-1-1-1-2-2-1-1-2-2-2-222221111-1-100000000000011−i3−i3i3i3−i3−i3i3i311-1-111-1-100000000000000i3−i3i3−i3000000
χ262222222222-12-2-2-2-22-1-1-1-1-1-1-1-2-2-1-1-2-2-2-222221111-1-100000000000011i3i3−i3−i3i3i3−i3−i311-1-111-1-100000000000000−i3i3−i3i3000000
χ2722222222-2-22-22222-22222222-2-2-2-2000000002222-2-2222222220000-2-20000000000000000-2-2-2-200000000000000000000
χ2822222222-2-22-22222-22222222-2-2-2-2000000002222-2-2-2-2-2-2-2-2-2-20000-2-20000000000000000222200000000000000000000
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χ3022222222-2-22-2-2-2-2-2-2222222222-2-200000000-2-2-2-2-2-20000000000002200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
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χ322222-2-2-2-2222-222-2-2-2222-2-2-2-2-22220000000022-2-2-2-2−2i−2i−2i−2i2i2i2i2i0000-2200000000000000002i2i−2i−2i00000000000000000000
χ332222-2-2-2-2222-2-2-222-2222-2-2-2-22-22200000000-2-222-2-20000000000002-2000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ342222-2-2-2-2222-2-2-222-2222-2-2-2-22-22200000000-2-222-2-20000000000002-200000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ352222-2-2-2-2-2-222-2-2222222-2-2-2-2-22-2-22i2i−2i−2i−2i−2i2i2i-2-22222000000000000-22000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ362222-2-2-2-2-2-222-2-2222222-2-2-2-2-22-2-2−2i−2i2i2i2i2i−2i−2i-2-22222000000000000-2200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ372222-2-2-2-2-2-2-1222-2-22-1-1-111112-2112i2i−2i−2i2i2i−2i−2i-1-111-1-1000000002i2i−2i−2i-11−i−i−i−iiiii−i−i−i−iiiii0000000000002-2-1-111000000
χ382222-2-2-2-2-2-2-1222-2-22-1-1-111112-2112i2i−2i−2i2i2i−2i−2i-1-111-1-100000000−2i−2i2i2i-11iiii−i−i−i−i−i−i−i−iiiii000000000000-2211-1-1000000
χ392222-2-2-2-2-2-2-1222-2-22-1-1-111112-211−2i−2i2i2i−2i−2i2i2i-1-111-1-1000000002i2i−2i−2i-11−i−i−i−iiiiiiiii−i−i−i−i000000000000-2211-1-1000000
χ402222-2-2-2-2-2-2-1222-2-22-1-1-111112-211−2i−2i2i2i−2i−2i2i2i-1-111-1-100000000−2i−2i2i2i-11iiii−i−i−i−iiiii−i−i−i−i0000000000002-2-1-111000000
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χ422222-2-2-2-2-2-2-12-2-2222-1-1-11111-22112i2i−2i−2i−2i−2i2i2i11-1-1-1-10000000000001-1−3−33333−3−3−i−iiiii−i−i00000000000000i3−i3−i3i3000000
χ432222-2-2-2-2-2-2-12-2-2222-1-1-11111-2211−2i−2i2i2i2i2i−2i−2i11-1-1-1-10000000000001-133−3−3−3−333ii−i−i−i−iii00000000000000i3−i3−i3i3000000
χ442222-2-2-2-2-2-2-12-2-2222-1-1-11111-2211−2i−2i2i2i2i2i−2i−2i11-1-1-1-10000000000001-1−3−33333−3−3ii−i−i−i−iii00000000000000−i3i3i3−i3000000
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χ4622-2-22i−2i2i−2i00202-22i−2i02-2-22i2i−2i−2i0000000000002-22i−2i002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−1−i1+i−1+i1−i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000000000−22i2−i200
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χ5222-2-2−2i2i−2i2i00202-2−2i2i02-2-2−2i−2i2i2i0000000000002-2−2i2i002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−1+i1−i−1−i1+i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000002−2i2−i200
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χ8244-4-4−4i4i−4i4i00-20-444i−4i0-2222i2i−2i−2i0000000000002-2−2i2i0000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ2200000000000000000000000000000000
χ834-44-44i−4i−4i4i004000000-44-44i−4i−4i4i0000000000000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000000000000
χ844-44-44i−4i−4i4i004000000-44-44i−4i−4i4i000000000000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000000000000
χ854-44-4−4i4i4i−4i004000000-44-4−4i4i4i−4i0000000000000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000000000000
χ864-44-4−4i4i4i−4i004000000-44-4−4i4i4i−4i000000000000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000000000000
χ874-4-4444-4-44-4-2-40000422-2-22-2200-2200004i−4i4i−4i0000-22000000000000000000000000−2i2i00−2i2i000000000000000000000000
χ884-4-4444-4-44-4-2-40000422-2-22-2200-220000−4i4i−4i4i0000-220000000000000000000000002i−2i002i−2i000000000000000000000000
χ894-4-4444-4-4-44-240000-422-2-22-22002-24-44-4000000002-20000000000000000000000-2200-2200000000000000000000000000
χ904-4-4444-4-4-44-240000-422-2-22-22002-2-44-44000000002-200000000000000000000002-2002-200000000000000000000000000
χ914-4-44-4-4444-4-240000-422-22-22-200-224i−4i−4i4i000000002-20000000000000000000000−2i2i002i−2i00000000000000000000000000
χ924-4-44-4-4444-4-240000-422-22-22-200-22−4i4i4i−4i000000002-200000000000000000000002i−2i00−2i2i00000000000000000000000000
χ934-4-44-4-444-44-2-40000422-22-22-2002-200004-4-440000-22000000000000000000000000-22002-2000000000000000000000000
χ944-4-44-4-444-44-2-40000422-22-22-2002-20000-444-40000-220000000000000000000000002-200-22000000000000000000000000
χ958-88-88i−8i−8i8i00-40000004-44−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8−8i8i8i−8i00-40000004-444i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000

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